# GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run

R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, N. Adhikari, R.

X. Adhikari, V. B. Adya, C. Affeldt, D. Agarwal, et al.

► To cite this version:

R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, et al., GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run. Physical Review X, 2023, 13 (4), pp.041039. 10.1103/PhysRevX.13.041039. hal-04651579

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# GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run

R. Abbott et al. *

(LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration)

<figure><img src="image_2.png" /></figure>

(Received 10 November 2021; accepted 5 June 2023; published 4 December 2023)

The third Gravitational-Wave Transient Catalog (GWTC-3) describes signals detected with Advanced LIGO and Advanced Virgo up to the end of their third observing run. Updating the previous GWTC-2.1, we present candidate gravitational waves from compact binary coalescences during the second half of the third observing run (O3b) between 1 November 2019, 15:00 Coordinated Universal Time (UTC) and 27 March 2020, 17:00 UTC. There are 35 compact binary coalescence candidates identified by at least one of our search algorithms with a probability of astrophysical origin $p_{astro} > 0.5$. Of these, 18 were previously reported as low-latency public alerts, and 17 are reported here for the first time. Based upon estimates for the component masses, our O3b candidates with $p_{astro} > 0.5$ are consistent with gravitational-wave signals from binary black holes or neutron-star–black-hole binaries, and we identify none from binary neutron stars. However, from the gravitational-wave data alone, we are not able to measure matter effects that distinguish whether the binary components are neutron stars or black holes. The range of inferred component masses is similar to that found with previous catalogs, but the O3b candidates include the first confident observations of neutron-star–black-hole binaries. Including the 35 candidates from O3b in addition to those from GWTC-2.1, GWTC-3 contains 90 candidates found by our analysis with $p_{astro} > 0.5$ across the first three observing runs. These observations of compact binary coalescences present an unprecedented view of the properties of black holes and neutron stars.

DOI: 10.1103/PhysRevX.13.041039

Subject Areas: Astrophysics, Gravitation

## I. INTRODUCTION

The Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) [1] and Advanced Virgo [2] detectors have revealed the Universe's abundance of gravitational-wave (GW) sources. Here, we present the third LIGO Scientific, Virgo, and KAGRA (LVK) Collaboration Gravitational-Wave Transient Catalog (GWTC-3), which records transient GW signals discovered up to the end of LIGO-Virgo's third observing run (O3). This updates the previous GWTC-2 [3] and GWTC-2.1 [4] by including signals found in the second part of O3 (O3b): This period comprises data taken between 1 November 2019, 15:00 Coordinated Universal Time (UTC) and 27 March 2020, 17:00 UTC. GWTC-3 adds 35 GW candidates from O3b that have an inferred probability of astrophysical compact binary coalescence (CBC) origin of $p_{astro} > 0.5$ based upon the results of our search algorithms. Additionally, there are 1048 subthreshold O3b candidates that do not

meet the CBC $p_{astro}$ threshold but have a false alarm rate (FAR) <2.0 day⁻¹. With the inclusion of O3b candidates, GWTC-3 is the most comprehensive set of GW observations presented to date, and it will further advance our understanding of astrophysics [5], fundamental physics [6], and cosmology [7].

GWTC-3 contains candidate GWs from CBCs: merging binaries consisting of black holes (BHs) and neutron stars (NSs). We analyze in detail the properties of candidates with $p_{astro} > 0.5$. Previously reported from O3b are the GW candidates GW200115_042309 and GW200105_162426, which are consistent with originating from neutron-star–black-hole binaries (NSBHs) [8]. The naming of these GW candidates follows the format GWYMMDD_hhmmss, encoding the date and UTC of the signal. In the GWTC-3 analysis, GW200105_162426 is found to have $p_{astro} < 0.5$; however, it remains a candidate of interest, and it is discussed in detail in later sections. In addition to GW200115_042309 and GW200105_162426, the O3b candidates include GW191219_163120 which is consistent with originating from a NSBH, and GW200210_092254 which could either be from a NSBH or from a binary black hole (BBH), as its less massive component has a mass ($m_2 = 2.83_{-0.42}^{+0.47} M_\odot$, quoting the median and symmetric 90% credible interval) that spans the range for possible NSs and BHs. All the other candidates are

<footnote>*Full author list given at the end of the paper.</footnote>

<footnote>Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.</footnote>
<figure><img src="image_3.png" /><figcaption>FIG. 1. The number of CBC detection candidates with a probability of astrophysical origin $p_{astro} > 0.5$ versus the detector network's effective surveyed time volume for BNS coalescences [3]. The colored bands indicate the different observing runs. The final datasets for O1, O2, O3a, and O3b consist of 49.4, 124.4, 149.8 (177.2), and 125.5 days (142.0 days) with at least two detectors (one detector) observing, respectively. The cumulative number of probable candidates is indicated by the solid black line, while the blue line, dark blue band, and light blue band are the median, 50% confidence interval, and 90% confidence interval for a Poisson distribution fit to the number of candidates at the end of O3b.</figcaption></figure>

consistent with being GW signals from BBHs, as their inferred component masses are above the theoretical upper limit of the NS maximum mass [9,10]. Among the O3b candidates with $p_{astro} > 0.5$, we expect approximately 10%–15% of candidates to be false alarms caused by instrumental noise fluctuations; a smaller, higher-purity sample of candidates could be obtained by adopting a stricter threshold.

During O3, low-latency public alerts were issued through Gamma-ray Coordinate Network (GCN) Notices and Circulars for GW candidates found by initial searches of the data [3,11]. These public alerts enable the astronomy community to search for multimessenger counterparts to potential GW signals. There were 39 low-latency candidates reported during O3b. Of these, 18 (excluding GW200105_162426) survive our detailed analyses to be included as potential CBC signals in GWTC-3. Additionally, GWTC-3 includes 17 candidates with $p_{astro} > 0.5$ that have not been previously presented. No confident multimessenger counterparts have currently been reported from the O3b candidates (as we review in Appendix A).

The total number of GW candidates with $p_{astro} > 0.5$ in GWTC-3 is 90, compared with three candidates found by LVK analyses after the end of the first observing run (O1) [12,13], 11 in GWTC-1 after the end of the second observing run (O2) [14], and 55 in GWTC-2.1 after the

end of the first part of O3 (O3a) [4]. Additional candidates have also been reported by other searches of public data [15–21]. The dramatic increase in the number of GW candidates during O3 was enabled by the improved sensitivity of the detector network. A conventional measure of sensitivity is the binary neutron star (BNS) inspiral range, which quantifies the average distance at which a fiducial $1.4M_{\odot} + 1.4M_{\odot}$ BNS could be detected with a signal-to-noise ratio (SNR) of 8 [22–24]. During O3b observations, the median BNS inspiral ranges for LIGO Livingston, LIGO Hanford, and Virgo were 133, 115, and 51 Mpc, respectively. In Fig. 1, we show the growth in the number of candidates in the LVK catalog across observing runs. Here, the search sensitivity is quantified by the BNS time volume, which should be approximately proportional to the search sensitivity to the overall astrophysical CBC population and hence to the number of detections [3]. The BNS time volume is defined as the observing time multiplied by the Euclidean sensitive volume for the detector network [24]. For O1 and O2, the observing time includes periods when at least two detectors were observing, and the Euclidean sensitive volume is the volume of a sphere with a radius equal to the BNS inspiral range of the second most sensitive detector in the network. For O3, to account for the potential of single-detector triggers, the observing time also includes periods when only one detector was observing, and the radius of the Euclidean sensitive volume is the greater of either (i) the BNS inspiral range of the second most sensitive detector, or (ii) the BNS inspiral range of the most sensitive detector divided by 1.5 (corresponding to a SNR threshold of 12) [3]. As the sensitivity of the detector network improves [25], the rate of discovery increases.

Further searches for GW transients in O3b data have been conducted focusing on intermediate-mass black-hole (IMBH) binaries (with a component $\gtrsim 65M_{\odot}$ and a final BH $\gtrsim 100M_{\odot}$) [26], subsolar-mass binaries [27], gravitationally lensed signals [28], signals coincident with gamma-ray bursts [29], cosmic strings [30], and both minimally modeled short-duration [$\lesssim O(1)$ s, such as from supernova explosions] [31] and long-duration [$\gtrsim O(1)$ s, such as from deformed magnetars or from accretion-disk instabilities] [32] signals. However, no high-significance candidates for types of signals other than the CBCs reported here have yet been found.

We begin with an overview of the status of the Advanced LIGO and Advanced Virgo detectors during O3b (Sec. II), and then we review the properties and quality of the data used in the analyses (Sec. III). We report the significance of the candidates identified by template-based and minimally modeled search analyses, and we compare this set of candidates to the low-latency public GW alerts issued during O3b (Sec. IV). We describe the inferred astrophysical parameters for the O3b candidates (Sec. V). Finally, we show the consistency of reconstructed
waveforms with those expected for CBCs (Sec. VI). In the Appendixes, we review public alerts and their multimes- senger follow-up (Appendix A); we describe commission- ing of the observatories for O3b (Appendix B); we detail the data-analysis methods used to assess data quality (Appendix C), search for signals (Appendix D), and infer source properties (Appendix E), and we discuss the difficulties in assuming a source type when performing a minimally modeled search analysis (Appendix F). A data release associated with this catalog is available from the Gravitational Wave Open Science Center (GWOSC) [33]; this includes calibrated strain time series around significant candidates, detection-pipeline results, parameter-estimation posterior samples, source localizations, and tables of inferred source parameters.

## II. INSTRUMENTS

The Advanced LIGO [1] and Advanced Virgo [2] instruments are kilometer-scale laser interferometers [34–36]. The advanced generation of interferometers began operations in 2015, and observing periods have been alternated with commissioning periods [25]. After O1 [13,37] and O2 [14], the sensitivity of the interferometers has improved significantly [3,38]. The main improvements were the adjustment of in-vacuum squeezed-light sources, or squeezers, for the LIGO Hanford and LIGO Livingston interferometers and the increase of the laser power in the Virgo interferometer. The instrumental

changes leading to improved sensitivities during O3b are discussed in Appendix B.

Figure 2 shows representative sensitivities during O3b for LIGO Hanford, LIGO Livingston, and Virgo, as characterized by the amplitude spectral density of the calibrated strain output. The sensitivity of the interferom- eters is primarily limited by the photon shot noise at high frequencies and by a superposition of several noise sources at lower frequencies [38]. The narrow-band features include vibrational modes of the suspension fibers, cali- bration lines, and 50- and 60-Hz electric power harmonics.

The left panel of Fig. 3 reports the evolution of the detectors’ sensitivity over time, as measured by the BNS inspiral range [22–24]. Gaps in the range curve are due to maintenance intervals, instrumental failures, and earth- quakes. The epochs marked on the graph correspond to improvements in LIGO Hanford (2 January 2020) and Virgo (28 January 2020) that are discussed in Appendix B. The median BNS inspiral range of Virgo over the whole of O3b was 51 Mpc, while the maximum value reached 60 Mpc. For comparison, the median range and the maximum range during O3a were 45 and 50 Mpc, respec- tively. The LIGO Hanford median BNS inspiral range improved from 108 Mpc in O3a to 115 Mpc in O3b, primarily due to the squeezed-light [39,40] source adjust- ments described in Appendix B. The LIGO Livingston median BNS inspiral range in O3b was 133 Mpc, consistent with the O3a value of 135 Mpc, with improvements due to squeezing counterbalanced by degradation primarily due to the reduced circulating power.

The duty cycles for the three interferometers, i.e., the fractions of the total O3b run duration in which the instruments were observing, were 79% (115.7 days) for LIGO Hanford, 79% (115.5 days) for LIGO Livingston, and 76% (111.3 days) for Virgo. As for previous observing runs, a subset of search analyses rejected additional data based on data-quality metrics, as described in Appendix C. The complete three-interferometer network was in observ- ing mode for 51.0% of the time (75.0 days). Moreover, for 96.6% of the time (142.0 days) at least one interferometer was observing, while for 85.3% (125.5 days) at least two interferometers were observing. For comparison, during O3a the duty cycles were 71%, 76%, and 76% for LIGO Hanford, LIGO Livingston, and Virgo, respectively; at least one interferometer was observing 96.8% of the time, and at least two interferometers were observing 81.8% of the time. The duty cycles for both the Hanford and Livingston interferometers improved from O3a to O3b. This demon- strates a clear improvement in robustness as higher micro- seism and storm activity were observed during O3b compared to O3a. While the fraction of time with at least one detector observing in O3a and O3b was comparable, the fraction of time with two instruments in observing mode increased, improving the performance of the network for coincident observations.

<figure><img src="image_4.png" /><figcaption>FIG. 2. Representative amplitude spectral density of the three interferometers’ strain sensitivity: LIGO Livingston 4 January 2020 02:53:42 UTC, LIGO Hanford 4 January 2020 18:20:42 UTC, Virgo 9 February 2020 01:16:00 UTC. From the amplitude spectral densities we estimate BNS inspiral ranges [22–24] of 114, 133, and 59 Mpc for LIGO Hanford, LIGO Livingston and Virgo, respectively.</figcaption></figure>
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>FIG. 3. The BNS inspiral range [22–24] of the LIGO and Virgo detectors. Left: the range evolution during O3b. Each data point corresponds to the median value of the range over a one-hour time segment. Right: distributions of the range and the median values for the entire duration of O3b; the data for Virgo are separately reported for the intervals before (I) and after (II) 28 January 2020 to illustrate changes in the range following detector improvements. An improvement in squeezer performance at LIGO Hanford is indicated at 2 January 2020.</figcaption></figure>

### III. DATA

Following the approach of previous analyses [3,4], we calibrate the data of each detector to GW strain and mitigate known instances of poor data quality before analyzing the LIGO and Virgo strain data for astrophysical sources. We include segments of data from each detector in our GW search analyses only when the detector was operating in a nominal state, and when there were no diagnostic measurements being made that might interfere with GW data collection.

Once data are recorded, they are calibrated in near-real time and in higher latency, as described in Sec. III A. We subtract noise from known long-duration, quasistationary instrumental sources [41–43]. We also exclude time periods containing identified and well-characterized noise likely to interfere with signal extraction from the astrophysical analyses, as described in Sec. III B. We thoroughly vet the data surrounding each GW candidate for evidence of transient noise, or glitches, or other anomalies that could impact accurate assessment of the candidate’s significance or accurate source-parameter estimation. For GW candidates found near in time or overlapping with transient noise, we apply additional data-processing steps, including the modeling and subtraction of glitches and linear subtraction of glitches using a witness time series [44], as described in Appendix C.

#### A. Calibration and noise subtraction

The dimensionless strain time series measured by the LIGO and Virgo detectors are an input to the astrophysical analyses. They are reconstructed from different output signals from the detectors and detailed modeling of the response of the detector [42,45]. The reconstructed strain

time series are timestamped following Global Positioning System (GPS) time, taking into account both the delays introduced in the synchronized distributed-clock timing system and data conditioning along the data-acquisition systems [46]. The detector responses are described as complex-valued frequency-dependent transfer functions [42,47]. Some control-system model parameters, such as the amount of light stored in the interferometer cavities and the gain of the actuators controlling the position of primary optics [1], vary slowly with time throughout operation of the interferometers. These parameters are monitored and, when possible, aspects of the calibration models are corrected in the strain reconstruction processing [42,45,48]. The analysis of the systematic error and uncertainty bounds for calibrated data throughout O3b is detailed in previous studies of LIGO [49,50] and Virgo data [51–53].

The three detectors use auxiliary lasers, known as photon calibrators [54–56], to induce fiducial displacement of test masses via photon radiation pressure. The fiducial displacements are known to better than 1% in LIGO and 1.8% in Virgo and are used to measure interferometer parameters’ variation with time, develop accurate models, and establish estimates of systematic error and associated uncertainty.

Calibration models are estimated from a collection of measurements that characterize the full detector response and from other measurements of individual components [42,49,50], such as the various electronics and suspension systems, gathered while the detector is offline (roughly once per week). An initial version of calibrated strain data is produced in low latency throughout an observing period, and the final calibration models are assembled after the completion of an observing period where the detector configuration was stable [45,53]. As needed, the GW strain data stream is then regenerated offline from the optical
power variations and the control signals, and the systematic error estimate is updated based on the model used for the offline strain reconstruction.

The best available strain data for each detector are used for both detection of GW signals and estimation of the sources' astrophysical parameters. For LIGO, the offline recalibrated strain data are used [49,50]. Initial analysis of Virgo's collection of validation measurements during the run did not motivate offline improvement to the low-latency strain data. Hence, Virgo's low-latency strain data are used for all analyses [51–53].

After the completion of the run, we identified a narrow-band increased systematic error between 46 and 51 Hz in Virgo data, mainly related to a control loop designed to damp mechanical resonances of the suspensions at 49 Hz [52]. This damping loop was added between O3a and O3b and ultimately improved the Virgo detector's sensitivity around 49 Hz. However, since this damping loop was not included in the calibration models, it resulted in an increased systematic error in the calibrated strain data around 49 Hz during O3b. There was also a large increase in the systematic error between 49.5 and 50.5 Hz related to a control loop designed to reduce the electric power-grid line [53]. Overall, the Virgo calibration errors in the band 46–51 Hz increase from 5% in amplitude and 35 mrad in phase to up to 40% in amplitude and 600 mrad in phase [53]. This narrow-band increased systematic error is accounted for in source-parameter estimation by notching out these frequencies (as described in Appendix E).

Known noise sources are subtracted from both the LIGO and Virgo strain data. The sinusoidal excitations used for calibration, known as calibration lines, are subtracted from the LIGO strain data. The 60-Hz electric power-grid lines are subtracted in the LIGO strain data along with the corresponding harmonics up to and including 300 Hz [43]. Additionally, noise contributions due to nonstationary coupling of the power grid are subtracted from the LIGO strain data [41,57]. Numerous noise sources that limit the Virgo detector's sensitivity are measured and linearly subtracted from the Virgo low-latency strain data using witness auxiliary sensors that measure the source of the noise [42, 53, 57, 59]. Calibration lines are also subtracted from the Virgo strain data.

All final source-parameter results, waveform reconstructions, and all but one search pipeline use strain data with all noise subtraction applied, as described above. The exception is the coherent WaveBurst (cWB) analysis [60], which searches for transient signals without assuming a model template. Following the GWTC-2 analysis [3], cWB uses LIGO strain data with the calibration lines and power-grid lines subtracted, but without the subtraction of the nonstationary coupling of the power grid. Comparison of analyses using different versions of noise subtraction indicates that the exact noise-subtraction procedure used does not significantly impact the cWB search results.

## B. Data quality

The most limiting source of noise for identification and analysis of transient GW sources is frequent, short-duration glitches in GW detector data [61–64]. A summary of glitch rates for the three observatories over O3b is shown in Fig. 4. Each point corresponds to the average number of glitches per minute with SNR $\rho > 6.5$ and peak frequency between 20 and 2048 Hz, estimated every 2048 s, as measured with the Omicron algorithm [65]. Continuous solid lines indicate the daily median of the corresponding glitch rate. In all three detectors, we observe relatively high glitch rates dominated by glitches below approximately 50 Hz corresponding to seasonally bad weather between the beginning of O3b and January 2020; some peaks in the glitch rate are also visible in Virgo data during the second

<figure><img src="image_7.png" /><figcaption>FIG. 4. The rate of single-interferometer glitches with SNR $\rho > 6.5$ and peak frequency between 20 and 2048 Hz identified by Omicron [65] in each detector during O3b. Each point represents the average rate per minute estimated over a 2048-s interval. Continuous curves represent the daily median of the rates. Black lines show the median rate over entire runs: dashed for O2, dotted for O3a, and dash-dotted for O3b. The vertical dashed lines indicate the implementation of reaction-chain (RC) tracking at the LIGO detectors, which reduces the rate of slow scattering glitches.</figcaption></figure>
half of O3b corresponding to persistent unstable weather conditions [66].

The horizontal black lines in Fig. 4 indicate the median glitch rates during O2 (dashed), O3a (dotted), and O3b (dash-dotted). With respect to O3a, both LIGO detectors register a modest glitch rate increase in O3b, with the rate changing from 0.29 to 0.32 min⁻¹ for Hanford and from 1.10 to 1.17 min⁻¹ for Livingston; this variation is much more pronounced for Virgo, which increased its glitch rate from 0.47 to 1.11 min⁻¹. As discussed for GWTC-2 [3], the increase in glitch rate in the two LIGO detectors between O2 and O3a is largely due to scattered-light glitches, and the decrease in Virgo's glitch rate between O2 and O3 is due to mitigation of several noise sources.

A large fraction of the O3b glitches captured in Fig. 4 are due to light scattering, as described in Appendix B. When the relative displacement between a mirror and a nearby moving reflective surface is ≳1 µm (the main laser wavelength) in amplitude, low-frequency ground motion can be up-converted to scattered-light glitches in the sensitive band of GW detector data [67,68]. During O3, approximately 44% and 45% of all the transient noise with SNR ρ > 10 at LIGO Livingston and LIGO Hanford, respectively, was due to light scattering. A high rate of scattered-light glitches is partly a consequence of weather-related high microseismic ground motion at the detector sites during O3b [63,69,70].

Two separate populations of transient noise due to light scattering known as slow scattering and fast scattering polluted LIGO data quality in O3. As illustrated in the spectrograms of Fig. 5, slow scattering noise appears as longer-duration (approximately 2.0–2.5 s) arches in the time-frequency plane, while fast scattering noise appears as short-duration (approximately 0.2–0.3 s) arches [70].

Slow scattering tends to occur when ground motion is high in the earthquake (0.03–0.1 Hz) or microseism (0.1–0.5 Hz) frequency bands. For the LIGO detectors, we find the presence of the slow scattering arches to be strongly correlated with the relative motion between the end test-mass chain and the reaction-mass chain of the optic suspension system used to control the motion of the test masses. This led to implementing reaction-chain tracking [71,72] in January 2020 to reduce this relative motion, as discussed in Appendix B. The rate of glitches associated with slow scattering significantly decreases after the implementation of the reaction-chain tracking [69].

Figure 4 shows that the overall O3b glitch rate significantly decreases for LIGO Hanford after the implementation of the reaction-chain tracking, changing from 0.82 to 0.18 min⁻¹. Correlated with this drop in glitch rate, the noise background becomes more stable and the average fraction of O3b public alerts that are retracted drops from 0.55 to 0.21.

Fast scattering is far more common at LIGO Livingston than at LIGO Hanford. During O3, it was the most frequent

<figure><img src="image_8.png" /><figcaption>FIG. 5. Representative spectrograms [73] of glitches caused by light scattering. Top: slow scattering appears as long-duration arches in the time-frequency plane. The multiple arches are due to multiple reflections between the test-mass optics and the scattering surface. During O3, slow scattering was the most frequent and second most frequent source of transient noise at LIGO Hanford and LIGO Livingston respectively. Bottom: as compared to slow scattering, fast scattering transients appear as short-duration, rapidly repeating arches.</figcaption></figure>

source of transient noise at Livingston. As shown in Fig. 5 and in Appendix C, fast scattering generally affects the GW data from 20 to 60 Hz, but occasionally manifests as high as 120 Hz. Increased ground motion in the anthropogenic (1–6 Hz) band, usually caused by bad weather conditions and human activity, especially with nearby heavy machinery such as logging trucks, increases the rate of fast scattering glitches. Physical environment and monitoring tests conducted at LIGO Livingston and LIGO Hanford found high-quality-factor mechanical resonances at frequencies close to 4 Hz [74,75] thought to be related to fast scattering. The fourth observing run (O4) upgrade plans include damping these resonances and studying the impact on the rate of fast scattering noise.

In Virgo, the initial high glitch rate and the subsequent peaks in Fig. 4 correspond predominantly to high numbers of glitches with central frequencies lower than 40 Hz. Across O3b, approximately 80% of glitches in Virgo with ρ > 6.5 have central frequencies lower than 40 Hz. These lower-frequency scattered-light glitches are largely the consequence of the activity of the sea, which is 15 km from the detector site [66,67].

All candidates reported in Tables I and II have undergone validation to check for plausible instrumental or environmental causes using the same methods as were applied to
<table><caption>TABLE I. Candidate GW signals. The time (UTC) of the signal is encoded in the name as GWYYMMDD_hmmss (e.g., GW200112_155838 occurred on 2020-01-12 at 15:58:38). The names of candidates not previously reported are given in bold. The detectors observing at the merger time of the candidate are indicated using single-letter identifiers (e.g., H for LIGO Hanford); these are not necessarily the same detectors that contributed triggers associated with the candidate. Where a candidate is found with $p_{astro}$ above the threshold value of 0.5 by at least one analysis but below the threshold by others, we include in italics the results from the other analyses, where available. Three center dots (...) indicate that a candidate was not found by an analysis. The two candidates labeled with a dagger (†) were found only above threshold in a single detector with the GslAL analysis, and the FAR estimates were made using significant extrapolation of the background data, meaning that single-detector candidates have higher uncertainty than coincident candidates. A conservative estimate of the FAR for these single-detector candidates is one per live time of the analysis; this is approximately 3.16 yr⁻¹ for both LIGO Hanford and LIGO Livingston.</caption><thead><tr><th rowspan="2">Name</th><th rowspan="2">Inst.</th><th colspan="3">cWB</th><th colspan="3">GslAL</th><th colspan="3">MBTA</th><th colspan="3">PyCBC-broad</th><th colspan="3">PyCBC-BBH</th></tr><tr><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th></tr></thead><tbody><tr><td>GW191103_012549</td><td>HL</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>27</td><td>9.0</td><td>0.13</td><td>4.8</td><td>9.3</td><td>0.77</td><td>0.46</td><td>9.3</td><td>0.94</td></tr><tr><td>GW191105_143521</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>24</td><td>10.0</td><td>0.07</td><td>0.14</td><td>10.7</td><td>&gt;0.99</td><td>0.012</td><td>9.8</td><td>&gt;0.99</td><td>0.036</td><td>9.8</td><td>&gt;0.99</td></tr><tr><td>GW191109_010717</td><td>HL</td><td>&lt;0.0011</td><td>15.6</td><td>&gt;0.99</td><td>0.0010</td><td>15.8</td><td>&gt;0.99</td><td>1.8 × 10<sup>-4</sup></td><td>15.2</td><td>&gt;0.99</td><td>0.096</td><td>13.2</td><td>&gt;0.99</td><td>0.047</td><td>14.4</td><td>&gt;0.99</td></tr><tr><td>GW191113_071753</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>26</td><td>9.2</td><td>0.68</td><td>1.1 × 10<sup>4</sup></td><td>8.3</td><td>&lt;0.01</td><td>1.2 × 10<sup>3</sup></td><td>8.5</td><td>&lt;0.01</td></tr><tr><td>GW191126_115259</td><td>HL</td><td>...</td><td>...</td><td>...</td><td>80</td><td>8.7</td><td>0.02</td><td>59</td><td>8.5</td><td>0.30</td><td>22</td><td>8.5</td><td>0.39</td><td>3.2</td><td>8.5</td><td>0.70</td></tr><tr><td>GW191127_050227</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>0.25</td><td>10.3</td><td>0.49</td><td>1.2</td><td>9.8</td><td>0.73</td><td>20</td><td>9.5</td><td>0.47</td><td>4.1</td><td>8.7</td><td>0.74</td></tr><tr><td>GW191129_134029</td><td>HL</td><td>...</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>13.3</td><td>&gt;0.99</td><td>0.013</td><td>12.7</td><td>&gt;0.99</td><td>&lt;2.6 × 10<sup>-5</sup></td><td>12.9</td><td>&gt;0.99</td><td>&lt;2.4 × 10<sup>-5</sup></td><td>12.9</td><td>&gt;0.99</td></tr><tr><td>GW191204_110529</td><td>HL</td><td>...</td><td>...</td><td>...</td><td>21</td><td>9.0</td><td>0.07</td><td>1.3 × 10<sup>4</sup></td><td>8.1</td><td>&lt;0.01</td><td>980</td><td>8.9</td><td>&lt;0.01</td><td>3.3</td><td>8.9</td><td>0.74</td></tr><tr><td>GW191204_171526</td><td>HL</td><td>&lt;8.7 × 10<sup>-4</sup></td><td>17.1</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>15.6</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>17.1</td><td>&gt;0.99</td><td>&lt;1.4 × 10<sup>-5</sup></td><td>16.9</td><td>&gt;0.99</td><td>&lt;1.2 × 10<sup>-5</sup></td><td>16.9</td><td>&gt;0.99</td></tr><tr><td>GW191215_223052</td><td>HLV</td><td>0.12</td><td>9.8</td><td>0.95</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>10.9</td><td>&gt;0.99</td><td>0.22</td><td>10.8</td><td>&gt;0.99</td><td>0.0016</td><td>10.3</td><td>&gt;0.99</td><td>0.28</td><td>10.2</td><td>&gt;0.99</td></tr><tr><td>GW191216_213338</td><td>HV</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>18.6</td><td>&gt;0.99</td><td>9.3 × 10<sup>-4</sup></td><td>17.9</td><td>&gt;0.99</td><td>0.0019</td><td>18.3</td><td>&gt;0.99</td><td>7.6 × 10<sup>-4</sup></td><td>18.3</td><td>&gt;0.99</td></tr><tr><td>GW191219_163120</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>4.0</td><td>...</td><td>8.9</td><td>0.82</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW191222_033537</td><td>HL</td><td>&lt;8.9 × 10<sup>-4</sup></td><td>11.1</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>12.0</td><td>&gt;0.99</td><td>0.0099</td><td>10.8</td><td>&gt;0.99</td><td>0.0021</td><td>11.5</td><td>&gt;0.99</td><td>9.8 × 10<sup>-5</sup></td><td>11.5</td><td>&gt;0.99</td></tr><tr><td>GW191230_180458</td><td>HLV</td><td>0.050</td><td>10.3</td><td>0.95</td><td>0.13</td><td>10.3</td><td>0.87</td><td>8.1</td><td>9.8</td><td>0.40</td><td>52</td><td>9.6</td><td>0.29</td><td>0.42</td><td>9.9</td><td>0.96</td></tr><tr><td>GW200112_155838</td><td>LV</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>17.6</td><td>&gt;0.99</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200115_042309</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>11.5</td><td>&gt;0.99</td><td>0.0055</td><td>11.2</td><td>&gt;0.99</td><td>&lt;1.2 × 10<sup>-4</sup></td><td>10.8</td><td>&gt;0.99</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200128_022011</td><td>HL</td><td>1.3</td><td>8.8</td><td>0.63</td><td>0.022</td><td>10.1</td><td>0.97</td><td>3.3</td><td>9.4</td><td>0.98</td><td>0.63</td><td>9.8</td><td>0.95</td><td>0.0043</td><td>9.9</td><td>&gt;0.99</td></tr><tr><td>GW200129_065458</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>26.5</td><td>&gt;0.99</td><td>...</td><td>...</td><td>...</td><td>&lt;2.3 × 10<sup>-5</sup></td><td>16.3</td><td>&gt;0.99</td><td>&lt;1.7 × 10<sup>-5</sup></td><td>16.2</td><td>&gt;0.99</td></tr><tr><td>GW200202_154313</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>11.3</td><td>&gt;0.99</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.025</td><td>10.8</td><td>&gt;0.99</td></tr><tr><td>GW200208_130117</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>0.0096</td><td>10.7</td><td>0.99</td><td>0.46</td><td>10.4</td><td>&gt;0.99</td><td>0.18</td><td>9.6</td><td>0.98</td><td>3.1 × 10<sup>-4</sup></td><td>10.8</td><td>&gt;0.99</td></tr><tr><td>GW200208_222617</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>160</td><td>8.2</td><td>&lt;0.01</td><td>420</td><td>8.9</td><td>0.02</td><td>...</td><td>...</td><td>...</td><td>4.8</td><td>7.9</td><td>0.70</td></tr><tr><td>GW200209_085452</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>0.046</td><td>10.0</td><td>0.95</td><td>12</td><td>9.7</td><td>0.97</td><td>550</td><td>9.2</td><td>0.04</td><td>1.2</td><td>9.2</td><td>0.89</td></tr><tr><td>GW200210_092254</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>1.2</td><td>9.5</td><td>0.42</td><td>...</td><td>...</td><td>...</td><td>17</td><td>8.9</td><td>0.53</td><td>7.7</td><td>8.9</td><td>0.54</td></tr><tr><td>GW200216_220804</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>0.35</td><td>9.4</td><td>0.77</td><td>2.4 × 10<sup>3</sup></td><td>8.8</td><td>0.02</td><td>970</td><td>9.0</td><td>&lt;0.01</td><td>7.8</td><td>8.7</td><td>0.54</td></tr><tr><td>GW200219_094415</td><td>HLV</td><td>0.77</td><td>9.7</td><td>0.85</td><td>9.9 × 10<sup>-4</sup></td><td>10.7</td><td>&gt;0.99</td><td>0.18</td><td>10.6</td><td>&gt;0.99</td><td>1.7</td><td>9.9</td><td>0.89</td><td>0.016</td><td>10.0</td><td>&gt;0.99</td></tr><tr><td>GW200220_061928</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>6.8</td><td>...</td><td>7.5</td><td>0.62</td></tr></tbody></table>

(Table continued)
<table><caption>TABLE I. (Continued)</caption><thead><tr><th rowspan="2">Name</th><th rowspan="2">Inst.</th><th colspan="3">cWB</th><th colspan="3">GstLAL</th><th colspan="3">MBTA</th><th colspan="3">PyCBC-broad</th><th colspan="3">PyCBC-BBH</th></tr><tr><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th></tr></thead><tbody><tr><td>GW200220_124850</td><td>HL</td><td>...</td><td>...</td><td>...</td><td>150</td><td>8.2</td><td>&lt;0.01</td><td>1.8 × 10<sup>3</sup></td><td>8.2</td><td>0.83</td><td>...</td><td>...</td><td>30</td><td>7.8</td><td>0.20</td></tr><tr><td>GW200224_222234</td><td>HLV</td><td>&lt;8.8 × 10<sup>-4</sup></td><td>18.8</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>18.9</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>19.0</td><td>&gt;0.99</td><td>&lt;8.2 × 10<sup>-5</sup></td><td>19.2</td><td>&gt;0.99</td><td>&lt;7.7 × 10<sup>-5</sup></td><td>18.6</td><td>&gt;0.99</td></tr><tr><td>GW200225_060421</td><td>HL</td><td>&lt;8.8 × 10<sup>-4</sup></td><td>13.1</td><td>&gt;0.99</td><td>0.079</td><td>12.9</td><td>0.93</td><td>0.0049</td><td>12.5</td><td>&gt;0.99</td><td>&lt;1.1 × 10<sup>-5</sup></td><td>12.3</td><td>&gt;0.99</td><td>4.1 × 10<sup>-5</sup></td><td>12.3</td><td>&gt;0.99</td></tr><tr><td>GW200302_015811</td><td>HV</td><td>...</td><td>...</td><td>...</td><td>0.11<sup>†</sup></td><td>10.6</td><td>0.91</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200306_093714</td><td>HL</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>410</td><td>8.5</td><td>0.81</td><td>3.4 × 10<sup>3</sup></td><td>7.8</td><td>&lt;0.01</td><td>24</td><td>8.0</td><td>0.24</td></tr><tr><td>GW200308_173609</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>680</td><td>8.1</td><td>&lt;0.01</td><td>6.9 × 10<sup>4</sup></td><td>8.3</td><td>0.24</td><td>770</td><td>7.9</td><td>&lt;0.01</td><td>2.4</td><td>8.0</td><td>0.86</td></tr><tr><td>GW200311_115853</td><td>HLV</td><td>&lt;8.2 × 10<sup>-4</sup></td><td>16.2</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>17.7</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>16.5</td><td>&gt;0.99</td><td>&lt;6.9 × 10<sup>-5</sup></td><td>17.0</td><td>&gt;0.99</td><td>&lt;7.7 × 10<sup>-5</sup></td><td>17.4</td><td>&gt;0.99</td></tr><tr><td>GW200316_215756</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>10.1</td><td>&gt;0.99</td><td>12</td><td>9.5</td><td>0.30</td><td>0.20</td><td>9.3</td><td>0.98</td><td>0.58</td><td>9.3</td><td>0.98</td></tr><tr><td>GW200322_091133</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>450</td><td>9.0</td><td>0.62</td><td>1.4 × 10<sup>3</sup></td><td>8.0</td><td>&lt;0.01</td><td>140</td><td>7.7</td><td>0.08</td></tr></tbody></table>

<table><caption>TABLE II. Marginal candidates found by the various analyses. The candidates in this table have a FAR below a threshold of 2.0 yr⁻¹ in at least one analysis, but were not found with *p*<sub>astro</sub> that meets our threshold for Table I (*p*<sub>astro</sub> > 0.5 from a search analysis, with the additional requirement that cWB candidates have a counterpart from a matched-filter analysis). The probability of astrophysical origin *p*<sub>astro</sub> quoted (i) assumes a CBC source, which may not always be applicable for candidates identified by the minimally modeled cWB analysis, and (ii) do not factor in data-quality information that was not used by the search algorithms. Further information on the cWB-only candidate 200214_224526 is available in Appendix F. Detector-identifying letters are the same as given in Table I. The instruments for each candidate are the ones which were operating at the time of the trigger, and are not necessarily the same as those which participated in the detection. The candidates are named according to the same convention as in Table I except that here we omit the GW prefix for the candidates found to be likely caused by instrumental artifacts, indicated with an asterisk (*). Where a candidate was seen below the FAR threshold in at least one analysis but above threshold in others, we include in italics the information on that trigger from the other analyses as well where available. As in Table I, the dagger (†) indicates a candidate found by a single detector with the GstLAL analysis.</caption><thead><tr><th rowspan="2">Name</th><th rowspan="2">Inst.</th><th colspan="3">cWB</th><th colspan="3">GstLAL</th><th colspan="3">MBTA</th><th colspan="3">PyCBC-broad</th></tr><tr><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th><th>FAR (yr<sup>-1</sup>)</th><th>SNR</th><th>p<sub>astro</sub></th></tr></thead><tbody><tr><td>GW191118_212859</td><td>LV</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>7.4 × 10<sup>5</sup></td><td>8.0</td><td>&lt;0.01</td><td>1.3</td><td>9.1</td><td>0.05</td></tr><tr><td>GW200105_162426</td><td>LV</td><td>...</td><td>...</td><td>...</td><td>0.20<sup>†</sup></td><td>13.9</td><td>0.36</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>200121_031748*</td><td>HV</td><td>...</td><td>...</td><td>...</td><td>58</td><td>9.1</td><td>0.02</td><td>1.1</td><td>10.7</td><td>0.23</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200201_203549</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>1.4</td><td>9.0</td><td>0.12</td><td>850</td><td>8.9</td><td>&lt;0.01</td><td>1.0 × 10<sup>3</sup></td><td>8.3</td><td>&lt;0.01</td></tr><tr><td>200214_224526*</td><td>HLV</td><td>0.13</td><td>13.1</td><td>0.91</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>200219_201407*</td><td>HLV</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.22</td><td>13.6</td><td>0.48</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200311_103121</td><td>HL</td><td>...</td><td>...</td><td>...</td><td>110</td><td>9.0</td><td>&lt;0.01</td><td>1.3</td><td>9.0</td><td>0.03</td><td>1.3</td><td>9.2</td><td>0.19</td></tr></tbody></table>
O3a candidates [3,63,64,76]. As discussed in Sec. IV D, none of the O3b candidates with CBC $p_{astro} > 0.5$ have evidence of instrumental origin, but we identify three marginal candidates (which do not meet the $p_{astro}$ threshold) as likely instrumental in origin. We also investigate non-Gaussian instrumental artifacts present in the data close to each candidate time that could bias measurements of the source parameters. In addition to the previously reported GW200105_162426 [8], we identify seven O3b candidates in Table I with nearby non-Gaussian artifacts that require mitigation before the data are further analyzed for source-parameter estimation. In order to mitigate instrument artifacts present near the time of these candidates, we follow a procedure similar to O3a [3]. Further details on data-quality mitigation techniques, including data-quality products publicly available via GWOSC, are given in Appendix C and in previous O3 analyses [3,63,77]. The specific mitigation methods applied for each of these candidates are described in Appendix E, with a summary for each candidate reported in Table XVI.

## IV. CANDIDATE IDENTIFICATION

Identification of candidates and assessment of their significance relative to the background of detector noise is the first step in extracting catalog results. This is followed by detailed analyses to estimate source properties (Sec. V) and reconstruct waveforms (Sec. VI). We use multiple search algorithms to identify potential GW candidates in our data. Searches are performed at two different latencies: online searches are run in near-real time as data are collected, and offline searches are completed later, using the final calibrated and cleaned dataset. The online analyses allow for the rapid release of public alerts associated with candidates to enable the search for multimessenger counterparts, as described in Appendix A. The offline analyses benefit from improved background statistics, extensive data calibration, vetting, and conditioning as described in Sec. III, and the ability to perform more computationally expensive calculations to separate signals from background given the relaxation of latency requirements. Because of these factors, the offline analyses are more sensitive than the online analyses. The increased sensitivity of the offline analyses means that differences in the final candidate list compared to the online results are expected. While the lowest FAR candidates are expected to remain significant, candidates with a higher FAR (e.g., near the threshold for public low-latency alerts) are more likely to have changes in significance when reevaluated offline, causing them to move above or below the corresponding threshold for inclusion in this catalog. The differences between the online and offline search results are further discussed in Sec. IV D 1. In this catalog, we report on the results of offline analyses performed after the end of O3b.

Our search analyses use different approaches to find candidates, either filtering the data using CBC waveform

templates to identify matches (described in Sec. IVA), or coherently searching data from the detector network for transient signals without assuming a waveform template (described in Sec. IV B). We use four pipelines to identify the candidates from O3b: three that search using CBC waveform templates, GstLAL [78–81], Multi-Band Template Analysis (MBTA) [82,83], and PyCBC [23,84–88], and one that searches for transient signals with minimal assumptions about sources, cWB [60,89,90]. The four pipelines used offline were also operated in online configurations, along with the waveform-based Summed Parallel Infinite Impulse Response (SPIIR) pipeline [91–93], to identify candidate GW signals in low latency. Of the four pipelines, cWB, GstLAL, and PyCBC are used for offline LVK analysis of O1 [13,94], O2 [14], and O3a [3,4] data, whereas MBTA was first used for offline analysis of O3a [4].

There are several technical and configuration differences across the pipelines used in the search analyses. While the CBC pipelines consider all possible (double or triple) detector combinations to form coincident triggers, cWB reports only analysis of pairs of detectors [31]. Another significant difference across pipelines is the data baseline used to assign FAR to candidates. The FAR is used as a measure of significance and defines how regularly we would expect to see a noise (nonastrophysical background) trigger with the same, or higher, ranking statistic as the candidate. GstLAL compares candidates to a global background from the full O3b time span, while cWB, MBTA, and PyCBC use local background from a typical time span of one to a few weeks. All pipelines estimate background distributions empirically from the O3b data. Further technical details of the search algorithms are given in Appendix D.

### A. Modeled search analyses for transient sources

The dedicated CBC search algorithms use matched filtering [95,96], identifying candidates by correlating the data with templates. We use sets of templates, or banks, that provide a discrete sampling of the parameter space defined by the binary component masses $m_1$ and $m_2$ (the primary and secondary masses defining $m_1 \ge m_2$), and the corresponding dimensionless spins $\vec{\chi}_1$ and $\vec{\chi}_2$.

The signals expected from CBCs are well characterized by combinations of the binary component parameters. To leading order, the phase evolution during inspiral of a binary is determined by the chirp mass [97,98],

$$ M = \frac{(m_1 m_2)^{3/5}}{(m_1 + m_2)^{1/5}}. \qquad (1) $$

We also use the total mass $M = m_1 + m_2$, and the mass ratio $q = m_2/m_1 \le 1$ to describe a binary system. The dimensionless component spin $\vec{\chi}_i = c\vec{S}_i/(Gm_i^2)$, where $\vec{S}_i$ is the spin angular momentum and $i = \{1, 2\}$, can theoretically range in magnitude from 0 (nonspinning) to
1 (Kerr limit) for BHs. The two spins are combined to form the effective inspiral spin [99,100] defined as

$$ \chi_{\text{eff}} = \frac{(m_1\vec{\chi}_1 + m_2\vec{\chi}_2) \cdot \hat{L}_N}{M}, \qquad (2) $$

where $\hat{L}_N$ is the unit vector in the direction of the Newtonian orbital angular momentum. In the modeled search analyses, the spins are assumed to be parallel to $\hat{L}_N$.

The banks cover systems with total masses, redshifted to the detector frame [101], ranging from a minimum value $2M_{\odot}$ for all pipelines to a maximum value of $200M_{\odot}$ (MBTA), $500M_{\odot}$ (PyCBC), or $758M_{\odot}$ (GstLAL). The minimum binary component mass is $1M_{\odot}$. Searches for binaries with component masses less than $1M_{\odot}$ have been completed in complementary analyses [27,102–106]. The PyCBC pipeline performs two search analyses. The first is an analysis encompassing a wide parameter space, allowing detection of many different types of CBC systems, which we refer to as the PyCBC-broad analysis. In addition to this broad analysis, PyCBC is also used in a different configuration, which we refer to as the PyCBC-BBH analysis: This analysis is restricted to BBH systems with total masses between $10M_{\odot}$ and $500M_{\odot}$, mass ratios in the range $1/3 \le q \le 1$, and component masses in the range $5M_{\odot} \le m_1 \le 350M_{\odot}$ and $m_2 \ge 5M_{\odot}$. This PyCBC-BBH analysis is designed to have higher sensitivity to BBH coalescences with component masses that are similar to those of the majority of previously detected systems. The range of templates is the same as used for the search of O3a [4].

For each template, the matched-filter correlation produces a time series of SNR values for each detector, and peaks in this time series form triggers. Only triggers with a matched-filter SNR exceeding a threshold are considered further in the analysis. This SNR threshold is $\rho > 4.0$ for PyCBC and GstLAL, and either 4.5 or 4.8, varying across the parameter space, for MBTA, MBTA and PyCBC assign a significance to triggers found with consistent binary parameters and times of arrival in at least two detectors, while GstLAL also does so for single-detector triggers. The SNR is combined with signal-consistency checks to rank triggers. Each pipeline uses a specific ranking statistic and background-estimation method to assess the significance and probability of astrophysical origin of these triggers and coincidences. Results from the various CBC search analyses are expected to differ due to differences in the waveform template banks and in algorithmic choices such as their ranking statistic and assumed signal distributions. Technical details of the GstLAL, MBTA, PyCBC, and (online-only) SPIIR analyses are given in Appendixes D 1, D 2, D 3, and D 4, respectively.

## B. Minimally modeled search analyses for transient sources

The cWB pipeline searches for generic, short transient signals across a network of GW detectors [60,107–110]. It provides rapid detection of GW transient signals with its online instance, and signal reconstructions and estimates of their significance with the version that runs offline on the final dataset. Designed to operate without a specific waveform model, cWB identifies coherent excess power in multiresolution time-frequency representations of the detector strain data. The SNR for each detector is estimated from the reconstructed waveforms, and the network SNR is calculated by combining the SNRs from the individual detectors. The cWB search analyses and reconstructions reported in this catalog primarily target BBH sources and are limited to the (16–512)-Hz range [60] to boost computational efficiency given the expected frequency range of BBH signals. The analysis is further split into two configurations that target high-mass (central frequency $f_c < 80$ Hz) and low-mass ($f_c > 80$ Hz) BBH systems [111]. Technical details of the cWB analysis are given in Appendix D 5.

## C. Probability of astrophysical origin

Our primary criterion for selecting candidates for further study is the probability of astrophysical origin $p_{\text{astro}}$. In contrast to FAR, this measure of significance incorporates our knowledge of the astrophysical rate of signals for different classes of binary systems. For instance, given the strongly differing rates of detectable signals from BBH and BNS coalescences, at a given FAR the probability of being an astrophysical signal will naturally be different between candidates consistent with BBH versus BNS origin. The probability of astrophysical origin is well suited for selecting candidates from a catalog containing results from observing runs of differing sensitivities. As the true alarm rate increases with improved sensitivity, the FAR needed for a candidate to reach a given $p_{\text{astro}}$ will change between observing runs.

In order to estimate $p_{\text{astro}}$ and its complement, the probability of terrestrial origin $p_{\text{terr}} = 1 - p_{\text{astro}}$, for a candidate, we model foreground and background event rates using a Poisson mixture formalism [112], as in previous LVK results [3,4,13,113,114]. Technical details of the calculation of $p_{\text{astro}}$ for each analysis pipeline are given in Appendix D 7.

For any candidate, $p_{\text{astro}}$ depends on the trigger's ranking statistic and where the trigger lies in the parameter space, i.e., the template with which it was found in a matched-filter analysis, or whether it was found in the low- or high-mass configurations of the cWB analysis. To calculate $p_{\text{astro}}$, we compare the expected number of astrophysical triggers and the expected number of background triggers for the given ranking statistic and measured parameters. The number of true astrophysical signals depends on merger
rates, which are jointly inferred as part of the $p_{astro}$ estimation method [3,13,112,115], using assumptions about the populations of astrophysical sources, and the detectors' and analysis' sensitivity, which is calculated using simulated signals. The number of background triggers is derived from the same background distribution used to estimate FAR by the search analyses.

As we cannot provide full source-parameter estimates for all candidates with FAR < 2.0 day⁻¹, we instead estimate the probability to originate from different categories of binary source (BNS, NSBH, and BBH). These probabilities are estimated by each pipeline separately and rely primarily on the template masses with which triggers are recovered (see Appendix D 7 for more details). For calculating $p_{astro}$, all triggers from the cWB analysis are assumed to be from BBH sources, as cWB has a reduced sensitivity to other population types. The source classes are defined in this calculation via an assumed boundary at $3M_\odot$: We consider any component with lower mass to be in the NS class and any component above as BH. These classes do not necessarily reflect the true division between NSs and BHs. The maximum mass of NSs is not currently known, but $3M_\odot$ should be a robust upper limit [9,10]. Therefore, the BBH category is intended to capture only BBHs, while the BNS and NSBH categories should capture all binaries with components that could be NSs in addition to possibly capturing some BBHs.

While the same approach is used by all analyses to assess $p_{astro}$ for their candidates, the detailed implementation varies. Besides differences in their ranking statistic definition, analyses divide the parameter space in different ways to compute $p_{astro}$, make slightly different assumptions about the astrophysical populations, have distinct responses to astrophysical sources, and have specific methods to evaluate their background. These differences will introduce a variation in results among pipelines. Each pipeline is subject to statistical and systematic uncertainties, such as how they respond to the observed noise fluctuations in ranking candidates, and the differences among pipelines mean that these uncertainties are not the same across pipelines. The details of these differences among pipelines are given in Appendix D. There is an extra uncertainty for single-detector candidates, where we can assume a conservative upper bound on FAR of 1 per observing time. However, we improve upon this estimate by extrapolating the noise background distribution. The $p_{astro}$ values given in Sec. IV D represent our current best estimates of the origin of candidates using the information available from search pipelines and detector characterization.

After its calculation, we must set a threshold on $p_{astro}$ for inclusion in the results presented here. As in previous publications [4,14], we choose the criterion $p_{astro} > 0.5$, such that the selected candidates are all inferred to have a higher probability of astrophysical origin than terrestrial. Values of $p_{astro}$ close to 1 are expected to be robust with

respect to uncertainties in the astrophysical populations, whereas cases for which $p_{astro}$ and $p_{terr}$ are comparable are sensitive to such uncertainties. Uncertainties are greater for candidates that, if astrophysical, have properties that correspond to a small number of detections in the overall population. The mass distributions for BBH sources are now sufficiently well constrained [116] such that we expect related uncertainties on $p_{astro}$ to be small for the bulk of this region; however, at particularly high masses these uncertainties are expected to be larger [4]. In contrast to the BBH population, the populations of BNS and NSBH sources remain poorly known [5]. Both the shape and the boundaries of the component mass distributions (especially for NSs) can have a significant impact on the value of $p_{astro}$ inferred for a BNS or NSBH candidate, and this uncertainty can be greater than 0.1 for moderate $p_{astro}$ values near the threshold of 0.5 [117]. We therefore expect that inferred values for $p_{astro}$ may change for less significant candidates as our understanding of the population evolves with further observations [118–120].

## D. Search results

There are many potential GW sources. Hence, in theory, GWTC-3 could contain a variety of source types. However, currently no high-significance (FAR < 10⁻² yr⁻¹) candidate transients have been reported for sources other than standard, quasicircular CBCs [26,29–32,121]. Therefore, we limit this GWTC-3 candidate list to the established source categories of BNSs, NSBHs, and BBHs.

Following GWTC-2.1 [4], we select candidates with a probability of an astrophysical CBC source $p_{astro} > 0.5$ for detailed analysis. In applying this criterion, we follow the method used in GWTC-1 [14] and consider only cWB candidates that also have a BBH counterpart from one of the matched-filter analyses (i.e., a time-coincident candidate with $p_{astro} > 0.1$). This is because cWB can potentially identify signals from a range of sources, but the calculation of $p_{astro}$ assumes a CBC source, and so additional confirmation is needed to verify that the candidate signal is consistent with a CBC origin. However, all O3b cWB candidates with $p_{astro} > 0.5$ also have $p_{astro} > 0.5$ from a matched-filter analysis anyway, except for 200214_224526, which is identified as being of instrumental origin [26]. The requirement that cWB candidates have a matched-filter counterpart is discussed further in Appendix F.

We identify 35 CBC candidates in O3b passing our threshold; these include 17 new candidates that were not found in low latency and are reported here for the first time. Significance estimates for the CBC candidates with probability of astrophysical origin $p_{astro} > 0.5$ are reported in Table I. We report the FAR, SNR, and $p_{astro}$ for each search analysis that finds a trigger when at least one analysis finds the candidate above the threshold for inclusion. Additionally, the SNRs reported from each
detector are given in Table XI of Appendix D 6. By comparing the sum of $p_{astro}$ values for candidates with $p_{astro} > 0.5$ to the number of such candidates for each analysis, we estimate that the expected contamination from triggers of terrestrial origin is approximately 10%–15%, or approximately four to six candidates. A higher-purity selection of candidates could be obtained by adopting a stricter selection criterion; for example, adopting a threshold of $p_{astro} > 0.9$ would result in a list of 22 O3b candidates. Probabilities for different source categories (BNS, NSBH, and BBH) are included in Table XIII in Appendix D 7. Updated values for $p_{astro}$ for O3a candidates are given in Table XV in Appendix D 7; there is no change to the list of O3a candidates with $p_{astro} > 0.5$ compared with GWTC-2.1 [4]. Results from O1 and O2 have not been recalculated [14]. The O3b candidates bring the total number of LVK-reported CBC candidates with $p_{astro} > 0.5$ to 90.

Marginal candidates with $p_{astro} < 0.5$ but FAR < 2.0 yr⁻¹ are discussed further in Sec. IV D 4. An extended list of candidates with FAR < 2.0 day⁻¹ is available from GWOSC [33] and discussed in Sec. IV D 5.

## 1. O3b online candidates

In O3b, there were 39 candidates reported in low latency (see Appendix A). All candidates identified by the online searches are assigned an internal identifier according to the date on which they occur, for example, S200105ae for GW200105_162426. These online analyses were carried out by the five pipelines: GstLAL, MBTAOnline, PyCBC Live, SPIR, and cWB. The overall FAR threshold for a public alert was set to one per two months (6 yr⁻¹) for CBC sources, meaning that once a trials factor is applied, there was a public-alert threshold of 1.2 yr⁻¹ for each online pipeline. Candidates found in low latency passing this threshold were disseminated to the public via GCN Notices and Circulars. This allowed for rapid follow-up searching for multimessenger counterparts. The online searches are necessarily limited in assessing the noise background as they can use only data collected up to the current time, and hence the FAR may be inaccurately calculated if there are sudden changes in the data quality. Among the 39 candidates reported in low latency, 16 were later retracted as they were likely due to detector noise.

None of the 16 retracted online candidates were found above our $p_{astro}$ threshold in the offline analyses, and thus are not included in Table I. There were five public candidates that did not meet the threshold for inclusion in Table I that were not retracted:

(i) S191205ah was found in low latency by GstLAL as a low-SNR ($\rho < 10$) single-detector candidate in LIGO Livingston with a FAR of 0.39 yr⁻¹. Such a FAR corresponds to modest significance, and thus, it is not surprising to find differences in the estimated significance by the initial online analysis and the end-of-run offline analyses. GstLAL did

not recover an offline trigger at this time with FAR < 2.0 day⁻¹.

(ii) S191213g was found in low latency by GstLAL in both LIGO Hanford and LIGO Livingston, with low network SNR and a modest FAR of 1.1 yr⁻¹. The offline trigger corresponding to this time was found with FAR > 2.0 day⁻¹, so it is not included in this catalog.

(iii) The NSBH candidate S200105ae (GW200105_162426 [8]) is reported as a marginal candidate (see Table II) and is further discussed below.

(iv) The cWB candidate S200114f was found online in the Hanford-Livingston-Virgo (HLV) three-detector network with FAR of 0.039 yr⁻¹, meeting the significance threshold for a public alert. It was considered for inclusion in the O3 search for short-duration minimally modeled transients [31], but that analysis was uniformly carried out on the Hanford-Livingston (HL) network, where the trigger did not qualify because of its low coherence (cWB network correlation coefficient $c_c < 0.8$). This candidate was discussed at length in the context of the search for IMBH binaries, where a potential instrumental origin was examined [26]. The analysis for the IMBH search was carried out using both the HL and HLV networks, and this candidate came out as marginally significant in the HLV network. In the analysis done for this catalog, this candidate was reported only by the cWB pipeline (which performed a two-detector analysis). Since the cWB $p_{astro}$ is low (<0.01), it does not meet the criteria for inclusion in Table I.

(v) S200213t was found in low latency by GstLAL as a low-SNR single-detector candidate in LIGO Hanford with a modest FAR of 0.56 yr⁻¹. Similar to S191205ah and S191213g, there was no offline trigger corresponding to S200213t with a FAR < 2.0 day⁻¹, so it does not appear in this catalog. Single-detector candidates, such as S191205ah and S200213t, are particularly susceptible to changes in significance due to relatively minor changes in data processing.

The remaining 18 candidates reported in low latency also appear in Table I.

## 2. New O3b candidates

The 17 new candidates listed in this catalog, not previously shared via GCN, are indicated in bold in Table I. Almost all of these candidates are found with modest significance. They are all coincident triggers involving at least both of the LIGO Hanford and Livingston detectors. The inferred source properties for all the new candidates (discussed in Sec. V) are consistent with BBH masses, with the exceptions of GW191219_163120 and GW200210_092254 that may be from NSBHs.
The identification of these new candidates can be attributed to a combination of factors: (i) Offline searches benefit from data with better calibration, cleaning and data-quality information, as well as improved algorithms, resulting in better background rejection, and (ii) using a $p_{astro}$ threshold allows us to highlight candidates in source-rich parts of the parameter space, including candidates with an (offline) FAR that would not meet the (online) threshold for public alerts.

### 3. Pipeline consistency

Not all candidates were found by all pipelines above the $p_{astro}$ threshold of 0.5: Of the 35 candidates, ten candidates were found by cWB, 21 candidates were found by GstLAL (including the two candidates found in a single detector), 20 candidates were found by MBTA, and 29 candidates were found by one or both of the PyCBC-BBH and PyCBC-broad analyses. Among the O3b candidates, 21 were found by two or more analysis pipelines, 15 by three or more pipelines, and nine by all pipelines. We expect the analyses to find different sets of candidates, due to different search methods, tuning, and configuration choices. The impact of differences among search pipelines will be largest for candidates with low SNR; thus, it is expected that such candidates may be identified by only a subset of pipelines. As methods used by different pipelines will be more or less effective in suppressing specific types of noise artifacts, and the sensitivity of different pipelines will have different dependencies on binary signal parameters, combining information from multiple pipelines should lead to a greater understanding of the population of astrophysical sources [122–124].

Some candidates are unique to a pipeline and not found by other pipelines:

(i) The GstLAL analysis found two unique candidates (see Appendix D 6); these are both single-detector candidates which had also been reported in low latency. As only GstLAL is configured to identify single-detector signals, we expect a difference among pipelines here.

(ii) The MBTA analysis found four unique candidates, newly reported here, all of which are quiet signals inferred to be from BBHs. These candidates have $p_{astro} > 0.5$ even though their FAR (integrated over a large parameter space) is high (see Appendix D 7 for further discussion), and their $p_{terr}$ is also significant. GW191113_071753 may have an unusual mass ratio, and GW200322_091133 has significant uncertainties for its inferred source properties (see Sec. V), which may make these signals (if real GWs) outliers in the astrophysical population; therefore, the $p_{astro}$ for these candidates is more uncertain than for more typical candidates [117].

(iii) The PyCBC analyses found eight unique candidates, all of which are newly reported in this catalog. Of these, two were found by both analyses, five were

found in the PyCBC-BBH analysis, and one in the PyCBC-broad analysis. All the candidates found uniquely by PyCBC are relatively quiet. The lowest FAR, and therefore most significant, is that of GW191103_012549: $0.46 \text{ yr}^{-1}$.

The candidate found only by the PyCBC-broad analysis, GW191219_163120, was found as a potential NSBH candidate, with a mass ratio of 0.09. The relatively large asymmetry in the component masses and low mass of the secondary component as identified by the search, $1.84M_{\odot}$, meant that the template was not analyzed in the PyCBC-BBH analysis. GW191219_163120, with redshifted chirp mass $4.69M_{\odot}$, is included in the same mass bin as the population of significant BBH candidates for the estimation of event rates entering $p_{astro}$ (see Appendix D 7). Such a simple binning scheme implies significant modeling uncertainty in $p_{astro}$ for candidates with parameters outside known populations: For instance, with a minor change in bin boundaries that puts the candidate in a different bin from the BBH population, its $p_{astro}$ would drop to 0.085. This example illustrates the sensitivity of $p_{astro}$ calculations to the assumed astrophysical population. For candidates at the edges of (or outside of) the confidently detected populations, like GW191219_163120, there may be large, model-dependent systematic uncertainties in $p_{astro}$. Future observations will reduce the uncertainty in the rate of similar mergers, and thus enable us to better quantify the origin of GW191219_163120.

Despite its high SNR, GW200129_065458 was identified only by a subset of the search analyses due to a specific set of circumstances. A data-quality issue in Livingston was reported through active Burst and CBC category 2 flags (and required mitigation, as described in Appendix C). The category 2 flags mean that the Livingston data were ignored by the cWB, MBTA, and PyCBC analyses. Moreover, in the MBTA analysis the combination of signal and noise was loud enough to trigger gating in Hanford, but not loud enough in Virgo to create a Hanford-Virgo (HV) coincidence in the high-threshold analysis performed without gating (see Appendix D 2 for details about the internal gating procedure used to remove suspected artifacts in the data). The PyCBC analyses still identified a candidate using only the HV data, but the network SNR is lower than reported by GstLAL on account of not including the Livingston data. In the cWB analysis, the trigger was reconstructed in the HV network but was rejected by the postproduction cuts. The differences in data handling among analyses are expected to lead to such differences in uncommon cases like this.

GW191109_010717, GW200208_222617, and GW200220_061928 are candidates with high-mass sources that potentially make them also relevant in the context of the search for IMBH binaries [26]. GW191109_010717 is a
highly significant candidate that was also found in that IMBH binary search with a FAR as low as $10^{-3}$ yr$^{-1}$, but has a joint posterior distribution for the primary and remnant masses that does not match the strict criteria to be considered as an IMBH binary [26] (see Sec. V). GW200208_222617 and GW200220_061928 are low-SNR candidates, which were not identified as significant in the IMBH search; this difference is likely due to different choices of ranking statistic between the two searches as well as differences between their noise backgrounds arising from a different parameter space.

## 4. Marginal candidates and GW200105_162426

In Table II, we report the marginal candidates that are found by each analysis below a FAR threshold of 2.0 yr$^{-1}$ but do not satisfy the $p_{astro}$ threshold for inclusion in Table I. The naming of these marginal candidates follows the same YYMMDD_hhmmss format as that described for the candidates of Table I, except omitting the GW prefix for the two candidates found to be caused by instrumental artifacts; for the other marginal candidates, we cannot exclude the possibility that they are quiet GW signals.

The marginal candidates 200121_031748, 200214_224526, and 200219_201407 were found to be likely caused by instrument artifacts. At the time of 200121_031748, LIGO Hanford data contain excess power consistent with a blip glitch, a common glitch in LIGO detector data [63,125]. At the time of 200214_224526, LIGO Livingston data contained significant excess noise due to fast scattering, while LIGO Hanford data showed evidence for a weak scattering arch; this candidate was further examined in the search for IMBH binaries [26], and is discussed in Appendix F. At the time of 200219_201407, LIGO Hanford data are highly nonstationary, with multiple loud glitches visible within 1 s of the candidate time.

The marginal candidate GW200311_103121 is found by both MBTA and PyCBC-broad with a template consistent with a (redshifted) chirp mass of $1.17M_{\odot}$ in both pipelines, and hence, if it were an astrophysical signal, its source would correspond to a BNS. Its chirp mass is close to that of GW170817 [126] and is consistent with Galactic BNSs [127]. Future observations will better constrain the mass distribution of BNS mergers and thus enable a more accurate assessment of the origin of this candidate.

The NSBH candidate GW200105_162426 [8] was found as a single-detector trigger by GstLAL with a FAR of $0.20$ yr$^{-1}$. This is comparable to the previously published value of $0.36$ yr$^{-1}$ [8], which used only data from the beginning of O3b until 22 January 2020. FARs are not assigned to single-detector triggers by the versions of the PyCBC and MBTA analyses used for these results (more recent developments do allow significance estimates for single-detector triggers in PyCBC searches [21,128]); however, GW200105_162426 was also seen by the PyCBC-broad and MBTA analyses as a Livingston trigger with SNRs

of 13.1 and 13.2, respectively, which were well above the backgrounds for triggers from similar templates. Based on $p_{astro}$, GW200105_162426 is listed here as a marginal candidate, despite it being a clear outlier from the background noise [8]. The marginal status of this candidate can at least in part be explained from the underlying assumptions in the candidate's FAR estimation and $p_{astro}$ computation.

The empirical background noise distribution available for evaluating the significance of single-detector candidates extends only as far as ranking statistics at which we see one noise trigger per observing time. In contrast, for multi-detector triggers, an extended background estimate can be obtained by constructing unphysical coincidences between triggers in different detectors. Consequently, for single-detector candidates like GW200105_162426 that lie outside the background noise distribution, the FAR estimation relies on an extrapolation. For triggers in the tail of the background distribution, this extrapolation comes with uncertainty that impacts the estimated FAR, and this uncertainty also propagates to the noise distribution used in the calculation of $p_{astro}$ [3,8].

Additionally, the $p_{astro}$ estimation for NSBH sources depends on the foreground distribution of ranking statistics as well as their merger rate. The former is subject to uncertainties coming from a lack of knowledge of the NSBH population, while the latter has large error bars due to a paucity of high-significance NSBH detections (order 1). Such uncertainties on $p_{astro}$ have a significant impact on marginal candidates whose $p_{astro}$ values hover around 0.5. As a consequence, the moderate $p_{astro}$ value assigned at this time to GW200105_162426 does not allow us to draw a firm conclusion on its origin. Future observations will likely shed more light on the true provenance of this and similar candidates.

## 5. Subthreshold candidates

Following GWTC-2.1 [4], we provide an extended list of O3b candidates with FAR less than $2.0$ day$^{-1}$ as part of the data products available from GWOSC [33]. In addition to the 35 O3b candidates with $p_{astro} > 0.5$ listed in Table I, and the seven marginal candidates with FAR less than $2.0$ yr$^{-1}$ listed in Table II, there are 1041 further subthreshold O3b candidates in the extended list (giving a total of 1083 O3b candidates in the data release) [33]. The subthreshold candidates have not been scrutinized for possible instrumental origin, but the purity of the sample is expected to be low: $\lesssim 0.01$ when considering all subthreshold candidates, as estimated in Sec. IV E 2.

For each subthreshold candidate, we provide estimates of their $p_{astro}$ (assuming a CBC source) and localization. Localization relies on the same tools that were used to provide low-latency localization for public GW alerts, namely, Bayestar [129,130] for GstLAL, MBTA, and PyCBC candidates, and cWB for its own candidates.
E. Search sensitivity

1. Sensitive hypervolume

To estimate the sensitivity of the search analyses, we calculate a sensitive time-volume hypervolume $\langle VT \rangle$ for each analysis during O3b. This hypervolume represents the sensitivity of each search analysis to a distribution of sources assumed to be uniformly distributed in comoving volume and source-frame time. The expected number of detections for a search analysis is

$$ \hat{N} = \langle VT \rangle R, \quad (3) $$

where R is the rate of signals per unit volume and unit observing time. The different pipeline live times affect their calculated $\langle VT \rangle$. The pipeline live times are 94.9 days (cWB), 142.0 days (GstLAL), 124.5 days (MBTA), and 124.2 days (both PyCBC analyses). To estimate $\langle VT \rangle$ for each analysis, we add simulated signals (referred to as injections) into the data and test how many are recovered. The injections we use are designed to cover the detected population of BBHs, BNSs, and NSBHs, and are described further in Appendix D 7. We use the same sets of simulated signals for each analysis to consistently measure $\langle VT \rangle$, but since the PyCBC-BBH and cWB analyses are designed to search for BBH signals, we use only injections in the designated BBH regions for these searches. Rather than consider the total rate of signals, we consider signals

corresponding to sources with specific masses to parametrize sensitivity to signals across parameter space.

In Table III, we report the O3b $\langle VT \rangle$ for simulated signals corresponding to sources with component masses close to the specified values. In Fig. 6, for each search, we show the variation in the O3b $\langle VT \rangle$ across the parameter space. The injections around the specified points are weighted so that they follow a log-normal distribution about the central mass with a width of 0.1. We also assume component spins are isotropically distributed with uniformly distributed magnitudes up to a maximum spin that depends on the source component mass; if $m_i < 2M_\odot$, we assume $\chi_{max} = 0.4$ and otherwise assume $\chi_{max} = 0.998$. We consider

(i) BHs at $35M_\odot$, which corresponds to a GW150914-like system [4,131], and is approximately where we infer a feature (potentially a bump or a break) in the BH mass spectrum [116];

(ii) BHs at $20M_\odot$, $10M_\odot$ and $5M_\odot$ to see how sensitivity varies across this range of previously detected BH masses;

(iii) NSs at $1.5M_\odot$, close to the canonical NS mass. We use several combinations of masses in order to assess our sensitivity to BNS, NSBH, and (relatively equal-mass) BBH systems. From the masses considered, the search sensitivity is greatest for $35M_\odot + 35M_\odot$ binaries in all analyses, although our detectors generally survey larger volume for higher-mass populations up to source component masses of approximately $100M_\odot$ [132,133]. Equivalent

<table><caption>TABLE III. Sensitive hypervolume from O3b for the various search analyses with $p_{astro} > 0.5$ at the assessed points in the mass parameter space. The Any results come from calculating the sensitive hypervolume for injections found by at least one search analysis. For each set of binary masses, the given values are the central points of a log-normal distribution with width 0.1. For some regions and analyses, few injections are recovered such that the sensitive hypervolume cannot be accurately estimated; these cases are indicated by three center dots (···). As an example of this, the PyCBC-BBH and cWB analyses analyzed only injections in the designated BBH set, and so no injections were found in the BNS or NSBH regions. The injected population is described in Appendix D 7.</caption><thead><tr><th colspan="3">Binary masses (M<sub>☉</sub>)</th><th colspan="6">Sensitive hypervolume (Gpc<sup>3</sup> yr)</th></tr><tr><th>m<sub>1</sub></th><th>m<sub>2</sub></th><th>M</th><th>cWB</th><th>GstLAL</th><th>MBTA</th><th>PyCBC-broad</th><th>PyCBC-BBH</th><th>Any</th></tr></thead><tbody><tr><td>35.0</td><td>35.0</td><td>30.5</td><td>2.6<sup>+0.1</sup><sub>-0.1</sub></td><td>4.1<sup>+0.1</sup><sub>-0.1</sub></td><td>3.3<sup>+0.2</sup><sub>-0.1</sub></td><td>3.3<sup>+0.1</sup><sub>-0.1</sub></td><td>4.3<sup>+0.2</sup><sub>-0.1</sub></td><td>5.3<sup>+0.1</sup><sub>-0.2</sub></td></tr><tr><td>35.0</td><td>20.0</td><td>22.9</td><td>1.35<sup>+0.09</sup><sub>-0.10</sub></td><td>2.3<sup>+0.2</sup><sub>-0.1</sub></td><td>1.8<sup>+0.1</sup><sub>-0.1</sub></td><td>1.9<sup>+0.1</sup><sub>-0.1</sub></td><td>2.5<sup>+0.1</sup><sub>-0.1</sub></td><td>3.1<sup>+0.1</sup><sub>-0.2</sub></td></tr><tr><td>35.0</td><td>1.5</td><td>5.2</td><td>...</td><td>1.8<sup>+0.2</sup><sub>-0.3</sub> × 10<sup>-2</sup></td><td>1.9<sup>+0.3</sup><sub>-0.3</sub> × 10<sup>-2</sup></td><td>3.1<sup>+0.3</sup><sub>-0.3</sub> × 10<sup>-2</sup></td><td>...</td><td>3.3<sup>+0.4</sup><sub>-0.3</sub> × 10<sup>-2</sup></td></tr><tr><td>20.0</td><td>20.0</td><td>17.4</td><td>0.56<sup>+0.04</sup><sub>-0.04</sub></td><td>1.34<sup>+0.06</sup><sub>-0.05</sub></td><td>1.10<sup>+0.05</sup><sub>-0.05</sub></td><td>1.14<sup>+0.05</sup><sub>-0.05</sub></td><td>1.42<sup>+0.06</sup><sub>-0.05</sub></td><td>1.71<sup>+0.06</sup><sub>-0.07</sub></td></tr><tr><td>20.0</td><td>10.0</td><td>12.2</td><td>0.24<sup>+0.03</sup><sub>-0.04</sub></td><td>0.60<sup>+0.05</sup><sub>-0.05</sub></td><td>0.51<sup>+0.05</sup><sub>-0.04</sub></td><td>0.56<sup>+0.05</sup><sub>-0.05</sub></td><td>0.65<sup>+0.05</sup><sub>-0.05</sub></td><td>0.77<sup>+0.06</sup><sub>-0.06</sub></td></tr><tr><td>20.0</td><td>1.5</td><td>4.2</td><td>...</td><td>1.9<sup>+0.2</sup><sub>-0.2</sub> × 10<sup>-2</sup></td><td>1.9<sup>+0.2</sup><sub>-0.2</sub> × 10<sup>-2</sup></td><td>2.7<sup>+0.2</sup><sub>-0.2</sub> × 10<sup>-2</sup></td><td>...</td><td>2.9<sup>+0.3</sup><sub>-0.2</sub> × 10<sup>-2</sup></td></tr><tr><td>10.0</td><td>10.0</td><td>8.7</td><td>6.8<sup>+0.8</sup><sub>-0.9</sub> × 10<sup>-2</sup></td><td>0.26<sup>+0.01</sup><sub>-0.02</sub></td><td>0.26<sup>+0.01</sup><sub>-0.02</sub></td><td>0.27<sup>+0.01</sup><sub>-0.02</sub></td><td>0.28<sup>+0.02</sup><sub>-0.02</sub></td><td>0.32<sup>+0.02</sup><sub>-0.01</sub></td></tr><tr><td>10.0</td><td>5.0</td><td>6.1</td><td>1.3<sup>+0.5</sup><sub>-0.4</sub> × 10<sup>-2</sup></td><td>0.10<sup>+0.02</sup><sub>-0.01</sub></td><td>0.10<sup>+0.02</sup><sub>-0.01</sub></td><td>0.12<sup>+0.01</sup><sub>-0.02</sub></td><td>0.11<sup>+0.02</sup><sub>-0.01</sub></td><td>0.13<sup>+0.02</sup><sub>-0.01</sub></td></tr><tr><td>10.0</td><td>1.5</td><td>3.1</td><td>...</td><td>1.6<sup>+0.1</sup><sub>-0.1</sub> × 10<sup>-2</sup></td><td>1.5<sup>+0.2</sup><sub>-0.1</sub> × 10<sup>-2</sup></td><td>1.8<sup>+0.1</sup><sub>-0.1</sub> × 10<sup>-2</sup></td><td>...</td><td>2.1<sup>+0.1</sup><sub>-0.1</sub> × 10<sup>-2</sup></td></tr><tr><td>5.0</td><td>5.0</td><td>4.4</td><td>5<sup>+1</sup><sub>-2</sub> × 10<sup>-3</sup></td><td>5.8<sup>+0.5</sup><sub>-0.4</sub> × 10<sup>-2</sup></td><td>4.5<sup>+0.4</sup><sub>-0.4</sub> × 10<sup>-2</sup></td><td>6.5<sup>+0.5</sup><sub>-0.4</sub> × 10<sup>-2</sup></td><td>5.0<sup>+0.5</sup><sub>-0.4</sub> × 10<sup>-2</sup></td><td>7.4<sup>+0.5</sup><sub>-0.5</sub> × 10<sup>-2</sup></td></tr><tr><td>5.0</td><td>1.5</td><td>2.3</td><td>...</td><td>1.12<sup>+0.05</sup><sub>-0.06</sub> × 10<sup>-2</sup></td><td>1.19<sup>+0.06</sup><sub>-0.05</sub> × 10<sup>-2</sup></td><td>1.21<sup>+0.06</sup><sub>-0.06</sub> × 10<sup>-2</sup></td><td>...</td><td>1.43<sup>+0.06</sup><sub>-0.06</sub> × 10<sup>-2</sup></td></tr><tr><td>1.5</td><td>1.5</td><td>1.3</td><td>...</td><td>2.7<sup>+0.1</sup><sub>-0.1</sub> × 10<sup>-3</sup></td><td>3.4<sup>+0.1</sup><sub>-0.1</sub> × 10<sup>-3</sup></td><td>3.5<sup>+0.1</sup><sub>-0.2</sub> × 10<sup>-3</sup></td><td>...</td><td>3.9<sup>+0.1</sup><sub>-0.2</sub> × 10<sup>-3</sup></td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>FIG. 6. Sensitive hypervolume $\langle VT \rangle$ from O3b for the various searches with $p_{astro} > 0.5$ at the assessed points in the mass parameter space. The Any results come from calculating the sensitive hypervolume for injections found by at least one search analysis. The plotted points correspond to the central points of the log-normal distributions (with widths 0.1) used for the calculation of $\langle VT \rangle$. Each point is marked by a pie chart, where the darker portion represents the fraction of the Any $\langle VT \rangle$ recovered. The color of the darker portion corresponds to the value of the sensitive $\langle VT \rangle$, as given by the scale bar. The values displayed are the same as those given in Table III.</figcaption></figure>

results for the whole of O3 are given in Table XIV in Appendix D 7 a.

The sensitivity results presented in Table III are obtained considering a detection threshold of $p_{astro} > 0.5$ calculated

as for our main results. The Any pipeline results come from taking the maximum $p_{astro}$ for an injection from across the analyses and represent our overall sensitivity to CBCs in the specified region.
The cWB results are obtained using the standard $p_{astro} > 0.5$ threshold; however, for candidates reported in Table I, we require that the cWB candidates must have an associated trigger from one of the matched-filter analyses, as the $p_{astro}$ calculation performed by cWB assumes that the signal is from a CBC. Therefore, we also investigate the cWB $\langle VT \rangle$ using a cut of $p_{astro} > 0.5$ from cWB together with the requirement that $p_{astro} > 0.1$ from at least one matched-filter analysis to match the main results. We find these values to be comparable; for example, the $\langle VT \rangle$ for the $5M_{\odot} + 5M_{\odot}$ bin is unchanged, at $5_{-2}^{+1} \times 10^{-3}$ Gpc$^3$ yr, and the $10M_{\odot} + 10M_{\odot}$ bin changes from $6.8_{-0.9}^{+0.8} \times 10^{-2}$ to $6.7_{-0.8}^{+0.9} \times 10^{-2}$ Gpc$^3$ yr. The largest change is in the highest-mass $35M_{\odot} + 35M_{\odot}$ bin, where the $\langle VT \rangle$ changes from $2.6_{-0.1}^{+0.1}$ to $2.5_{-0.1}^{+0.1}$ Gpc$^3$ yr. Overall, adding the requirement that there be a CBC counterpart to cWB candidates makes little difference to the search sensitivity calculated from our CBC injections.

## 2. Subthreshold signal count via search sensitivities

The search sensitivities may also be calculated at the threshold of FAR < 2.0 day$^{-1}$ corresponding to the sub-threshold candidate set, enabling us to self-consistently estimate the number of astrophysical signals among these 1048 candidates. For an individual search pipeline, if the source population assumed in the $p_{astro}$ calculation is sufficiently close to the (unknown) true population, then the sum of $p_{astro}$ values over a candidate set gives the expectation of the number of true signals in the set [134]. This count of signals is itself a realization of a Poisson process with a mean proportional to the pipeline's $\langle VT \rangle$ for the true signal population. Hence, if the true population were known, we could scale the sum of $p_{astro}$ values for each pipeline by its $\langle VT \rangle$ to obtain an estimate of the signal count at a given threshold for the combined Any pipeline analysis.

In lieu of the true population, we take as reference the $\langle VT \rangle$ values for the $35M_{\odot} + 35M_{\odot}$ point, as representing the largest proportion of detected signals. The resulting estimated signal counts for Any pipeline are consistent across pipelines within statistical uncertainties. Consistent and similar counts are also obtained for the modeled pipelines if the $20M_{\odot} + 20M_{\odot}$ or $10M_{\odot} + 10M_{\odot}$ points are taken as a reference, indicating that the result is not strongly sensitive to an assumed BBH mass distribution; the counts for cWB do vary, but the cWB contribution to the Any pipeline sensitivity varies significantly across the parameter space and is subdominant to the modeled pipelines for the lower-mass BBH points. The number of subthreshold signals is then the difference between signal counts (excluding the marginal candidates found to be likely caused by instrumental artifacts) for the thresholds FAR < 2.0 day$^{-1}$ and $p_{astro} > 0.5$, which averaged over pipelines yields approximately 7, with an

expected uncertainty of approximately $\sqrt{7}$. This estimate is consistent with the ratio of $\langle VT \rangle$ values for Any pipeline between the two thresholds, which is 1.2–1.3 for the BBH mass points.

## V. SOURCE PROPERTIES

Having identified candidate signals, we perform a coherent analysis of the data from the GW detector network to infer the properties of each source. Information about the source parameters is encoded within the amplitude and phase of the GW signal recorded by each detector in the network. To extract this information, we match model waveform templates to the observed data to calculate the posterior probability of a given set of parameters [135], assuming that the noise is Gaussian, stationary, and uncorrelated between detectors [96]. We use the waveform models IMRPhenomXPHM [136] and SEOBNRv4PHM [137] to describe BBH systems, and IMRPhenomNSBH [138] and SEOBNRv4_ROM_NRTidalv2_NSBH [139] to describe matter effects in NSBH systems. All templates assume quasicircular binaries, with the BBH models including the effects of spin precession and higher-order multipole moments [136,137,140,141]. As the higher-order multipole moments and spin precession effects incorporated into the BBH waveform templates are more important in describing the signal than the NSBH matter effects, we preferentially quote results using the BBH waveforms [8]. We use an equal combination of IMRPhenomXPHM and SEOBNRv4PHM samples [142,143]. Potential systematic uncertainties from differences in waveform modeling are discussed in Sec. V E. Analyses using the IMRPhenomXPHM or NSBH waveforms are performed with the Bilby family of codes [144–146] and analyses using the SEOBNRv4PHM waveforms are performed with RIFT [147–149]. The analysis closely follows the practices from previous studies [4,131], and further details are presented in Appendix E.

A summary of key results for O3b candidates is given in Table IV and shown in Figs. 7–9. We show results for the O3b candidates with $p_{astro} > 0.5$ plus GW200105_162426, which, despite being a marginal candidate, is a clear outlier from the noise background [8]. On account of its low $p_{astro}$, we highlight GW200105_162426 in figures and tables. We similarly highlight GW191219_163120 because, as discussed in Sec. IV D 3, the calculated $p_{astro}$ is especially sensitive to the adopted population model, and, as discussed below, there is significant posterior support for mass ratios outside the range of calibration for the waveform models. Following previous analyses [3,4], results are calculated using default priors that are intended to not make strong assumptions about the underlying astrophysical population (e.g., uniform priors are used for redshifted component masses, an isotropic distribution is used for spin orientations, and it is assumed that sources are uniformly distributed in comoving volume and time).
<table><caption>TABLE IV. Median and 90% symmetric credible intervals for selected source parameters, and the 90% credible area for the sky localization for O3b candidates with $p_{astro} > 0.5$ plus GW200105_162426. We highlight with italics GW200105_162426 as it has $p_{astro} < 0.5$, as well as GW191219_163120 because of significant uncertainty in its $p_{astro}$ and because it has significant posterior support outside of mass ratios where the waveform models are calibrated. An asterisk (*) is used to indicate candidates for which the posterior distributions are dominated by potentially unphysical, low-likelihood modes at large distances and high masses, and are particularly prior sensitive. The columns show source total mass $M$, chirp mass $M$, component masses $m_i$, effective inspiral spin $\chi_{eff}$, luminosity distance $D_L$, redshift $z$, final mass $M_f$, final spin $\chi_f$, sky localization $\Delta\Omega$, and the network matched-filter SNR. All quoted results are calculated using BBH waveform models; values come from averaging IMRPhenomXPHM and SEOBNRv4PHM results, except for the SNR (which is given for IMRPhenomXPHM because the RIFT analysis used for SEOBNRv4PHM does not output this quantity).</caption><thead><tr><th>Candidate</th><th>M(M<sub>☉</sub>)</th><th>M(M<sub>☉</sub>)</th><th>m<sub>1</sub>(M<sub>☉</sub>)</th><th>m<sub>2</sub>(M<sub>☉</sub>)</th><th>χ<sub>eff</sub></th><th>D<sub>L</sub>(Gpc)</th><th>z</th><th>M<sub>f</sub>(M<sub>☉</sub>)</th><th>χ<sub>f</sub></th><th>ΔΩ(deg<sup>2</sup>)</th><th>SNR</th></tr></thead><tbody><tr><td>GW191103_012549</td><td>20.0<sup>+3.7</sup><sub>-1.8</sub></td><td>8.34<sup>+0.66</sup><sub>-0.57</sub></td><td>11.8<sup>+6.2</sup><sub>-2.2</sub></td><td>7.9<sup>+1.7</sup><sub>-2.4</sub></td><td>0.21<sup>+0.16</sup><sub>-0.10</sub></td><td>0.99<sup>+0.50</sup><sub>-0.47</sub></td><td>0.20<sup>+0.09</sup><sub>-0.09</sub></td><td>19.0<sup>+3.8</sup><sub>-1.7</sub></td><td>0.75<sup>+0.06</sup><sub>-0.05</sub></td><td>2500</td><td>8.9<sup>+0.3</sup><sub>-0.5</sub></td></tr><tr><td>GW191105_143521</td><td>18.5<sup>+2.1</sup><sub>-1.3</sub></td><td>7.82<sup>+0.61</sup><sub>-0.45</sub></td><td>10.7<sup>+3.7</sup><sub>-1.6</sub></td><td>7.7<sup>+1.4</sup><sub>-1.9</sub></td><td>-0.02<sup>+0.13</sup><sub>-0.09</sub></td><td>1.15<sup>+0.43</sup><sub>-0.48</sub></td><td>0.23<sup>+0.07</sup><sub>-0.09</sub></td><td>17.6<sup>+2.1</sup><sub>-1.2</sub></td><td>0.67<sup>+0.04</sup><sub>-0.05</sub></td><td>640</td><td>9.7<sup>+0.3</sup><sub>-0.5</sub></td></tr><tr><td>GW191109_010717</td><td>112<sup>+20</sup><sub>-16</sub></td><td>47.5<sup>+9.6</sup><sub>-7.5</sub></td><td>65<sup>+11</sup><sub>-11</sub></td><td>47<sup>+15</sup><sub>-13</sub></td><td>-0.29<sup>+0.42</sup><sub>-0.31</sub></td><td>1.29<sup>+1.13</sup><sub>-0.65</sub></td><td>0.25<sup>+0.18</sup><sub>-0.12</sub></td><td>107<sup>+18</sup><sub>-15</sub></td><td>0.61<sup>+0.18</sup><sub>-0.19</sub></td><td>1600</td><td>17.3<sup>+0.5</sup><sub>-0.5</sub></td></tr><tr><td>GW191113_071753</td><td>34.5<sup>+10.5</sup><sub>-9.8</sub></td><td>10.7<sup>+1.1</sup><sub>-1.0</sub></td><td>29<sup>+12</sup><sub>-14</sub></td><td>5.9<sup>+4.4</sup><sub>-1.3</sub></td><td>0.00<sup>+0.37</sup><sub>-0.29</sub></td><td>1.37<sup>+1.15</sup><sub>-0.62</sub></td><td>0.26<sup>+0.18</sup><sub>-0.11</sub></td><td>34<sup>+11</sup><sub>-10</sub></td><td>0.45<sup>+0.33</sup><sub>-0.11</sub></td><td>3600</td><td>7.9<sup>+0.5</sup><sub>-1.1</sub></td></tr><tr><td>GW191126_115259</td><td>20.7<sup>+3.4</sup><sub>-2.0</sub></td><td>8.65<sup>+0.95</sup><sub>-0.71</sub></td><td>12.1<sup>+5.5</sup><sub>-2.2</sub></td><td>8.3<sup>+1.9</sup><sub>-2.4</sub></td><td>0.21<sup>+0.15</sup><sub>-0.11</sub></td><td>1.62<sup>+0.74</sup><sub>-0.74</sub></td><td>0.30<sup>+0.12</sup><sub>-0.13</sub></td><td>19.6<sup>+3.5</sup><sub>-2.0</sub></td><td>0.75<sup>+0.06</sup><sub>-0.05</sub></td><td>1400</td><td>8.3<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>GW191127_050227</td><td>80<sup>+39</sup><sub>-22</sub></td><td>29.9<sup>+11.7</sup><sub>-9.1</sub></td><td>53<sup>+47</sup><sub>-20</sub></td><td>24<sup>+17</sup><sub>-14</sub></td><td>0.18<sup>+0.34</sup><sub>-0.36</sub></td><td>3.4<sup>+3.1</sup><sub>-1.9</sub></td><td>0.57<sup>+0.40</sup><sub>-0.29</sub></td><td>76<sup>+39</sup><sub>-21</sub></td><td>0.75<sup>+0.13</sup><sub>-0.29</sub></td><td>980</td><td>9.2<sup>+0.7</sup><sub>-0.6</sub></td></tr><tr><td>GW191129_134029</td><td>17.5<sup>+2.4</sup><sub>-1.2</sub></td><td>7.31<sup>+0.43</sup><sub>-0.28</sub></td><td>10.7<sup>+4.1</sup><sub>-2.1</sub></td><td>6.7<sup>+1.5</sup><sub>-1.7</sub></td><td>0.06<sup>+0.16</sup><sub>-0.08</sub></td><td>0.79<sup>+0.26</sup><sub>-0.33</sub></td><td>0.16<sup>+0.05</sup><sub>-0.06</sub></td><td>16.8<sup>+2.5</sup><sub>-1.2</sub></td><td>0.69<sup>+0.03</sup><sub>-0.05</sub></td><td>850</td><td>13.1<sup>+0.2</sup><sub>-0.3</sub></td></tr><tr><td>GW191204_110529</td><td>47.1<sup>+9.1</sup><sub>-7.8</sub></td><td>19.8<sup>+3.6</sup><sub>-1.3</sub></td><td>27.3<sup>+10.8</sup><sub>-5.9</sub></td><td>19.2<sup>+5.5</sup><sub>-6.0</sub></td><td>0.05<sup>+0.25</sup><sub>-0.26</sub></td><td>1.9<sup>+1.7</sup><sub>-1.9</sub></td><td>0.34<sup>+0.25</sup><sub>-0.18</sub></td><td>45.0<sup>+8.7</sup><sub>-7.5</sub></td><td>0.71<sup>+0.11</sup><sub>-0.11</sub></td><td>3400</td><td>8.9<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>GW191204_171526</td><td>20.19<sup>+1.64</sup><sub>-0.95</sub></td><td>8.56<sup>+0.41</sup><sub>-0.28</sub></td><td>11.7<sup>+3.3</sup><sub>-1.7</sub></td><td>8.4<sup>+1.3</sup><sub>-1.7</sub></td><td>0.16<sup>+0.08</sup><sub>-0.05</sub></td><td>0.64<sup>+0.20</sup><sub>-0.26</sub></td><td>0.13<sup>+0.04</sup><sub>-0.05</sub></td><td>19.18<sup>+1.71</sup><sub>-0.93</sub></td><td>0.73<sup>+0.04</sup><sub>-0.03</sub></td><td>310</td><td>17.4<sup>+0.2</sup><sub>-0.3</sub></td></tr><tr><td>GW191215_223052</td><td>43.3<sup>+5.3</sup><sub>-4.3</sub></td><td>18.4<sup>+2.2</sup><sub>-1.7</sub></td><td>24.9<sup>+7.1</sup><sub>-4.1</sub></td><td>18.1<sup>+3.8</sup><sub>-4.1</sub></td><td>-0.04<sup>+0.17</sup><sub>-0.21</sub></td><td>1.93<sup>+0.89</sup><sub>-0.86</sub></td><td>0.35<sup>+0.13</sup><sub>-0.14</sub></td><td>41.4<sup>+5.1</sup><sub>-4.1</sub></td><td>0.68<sup>+0.07</sup><sub>-0.07</sub></td><td>530</td><td>11.2<sup>+0.3</sup><sub>-0.4</sub></td></tr><tr><td>GW191216_213338</td><td>19.80<sup>+2.70</sup><sub>-0.93</sub></td><td>8.33<sup>+0.22</sup><sub>-0.19</sub></td><td>12.1<sup>+4.6</sup><sub>-2.2</sub></td><td>7.7<sup>+1.6</sup><sub>-1.9</sub></td><td>0.11<sup>+0.13</sup><sub>-0.06</sub></td><td>0.34<sup>+0.12</sup><sub>-0.13</sub></td><td>0.07<sup>+0.02</sup><sub>-0.03</sub></td><td>18.87<sup>+2.81</sup><sub>-0.93</sub></td><td>0.70<sup>+0.03</sup><sub>-0.04</sub></td><td>910</td><td>18.6<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>GW191219_163120</td><td>32.3<sup>+2.2</sup><sub>-2.7</sub></td><td>4.31<sup>+0.12</sup><sub>-0.17</sub></td><td>31.1<sup>+2.2</sup><sub>-2.8</sub></td><td>1.17<sup>+0.07</sup><sub>-0.06</sub></td><td>0.00<sup>+0.07</sup><sub>-0.09</sub></td><td>0.55<sup>+0.24</sup><sub>-0.16</sub></td><td>0.11<sup>+0.05</sup><sub>-0.03</sub></td><td>32.2<sup>+2.2</sup><sub>-2.7</sub></td><td>0.14<sup>+0.06</sup><sub>-0.06</sub></td><td>1500</td><td>9.1<sup>+0.5</sup><sub>-0.8</sub></td></tr><tr><td>GW191222_033537</td><td>79<sup>+16</sup><sub>-11</sub></td><td>33.8<sup>+7.1</sup><sub>-5.0</sub></td><td>45.1<sup>+10.9</sup><sub>-8.0</sub></td><td>34.7<sup>+9.3</sup><sub>-10.5</sub></td><td>-0.04<sup>+0.20</sup><sub>-0.25</sub></td><td>3.0<sup>+1.7</sup><sub>-1.7</sub></td><td>0.51<sup>+0.23</sup><sub>-0.26</sub></td><td>75.5<sup>+15.3</sup><sub>-9.9</sub></td><td>0.67<sup>+0.08</sup><sub>-0.11</sub></td><td>2000</td><td>12.5<sup>+0.2</sup><sub>-0.3</sub></td></tr><tr><td>GW191230_180458</td><td>86<sup>+19</sup><sub>-12</sub></td><td>36.5<sup>+8.2</sup><sub>-5.6</sub></td><td>49.4<sup>+14.0</sup><sub>-9.6</sub></td><td>37<sup>+11</sup><sub>-12</sub></td><td>-0.05<sup>+0.26</sup><sub>-0.31</sub></td><td>4.3<sup>+2.1</sup><sub>-1.9</sub></td><td>0.69<sup>+0.26</sup><sub>-0.27</sub></td><td>82<sup>+17</sup><sub>-11</sub></td><td>0.68<sup>+0.11</sup><sub>-0.13</sub></td><td>1100</td><td>10.4<sup>+0.3</sup><sub>-0.4</sub></td></tr><tr><td>GW200105_162426</td><td>11.0<sup>+1.5</sup><sub>-1.4</sub></td><td>3.42<sup>+0.08</sup><sub>-0.08</sub></td><td>9.1<sup>+1.7</sup><sub>-1.7</sub></td><td>1.91<sup>+0.33</sup><sub>-0.24</sub></td><td>0.00<sup>+0.13</sup><sub>-0.18</sub></td><td>0.27<sup>+0.12</sup><sub>-0.11</sub></td><td>0.06<sup>+0.02</sup><sub>-0.02</sub></td><td>10.8<sup>+1.5</sup><sub>-1.4</sub></td><td>0.43<sup>+0.05</sup><sub>-0.02</sub></td><td>9600</td><td>13.7<sup>+0.2</sup><sub>-0.4</sub></td></tr><tr><td>GW200112_155838</td><td>63.9<sup>+5.7</sup><sub>-4.6</sub></td><td>27.4<sup>+2.6</sup><sub>-2.1</sub></td><td>35.6<sup>+6.7</sup><sub>-4.5</sub></td><td>28.3<sup>+4.4</sup><sub>-5.9</sub></td><td>0.06<sup>+0.15</sup><sub>-0.08</sub></td><td>1.25<sup>+0.43</sup><sub>-0.46</sub></td><td>0.24<sup>+0.07</sup><sub>-0.08</sub></td><td>60.8<sup>+5.3</sup><sub>-4.3</sub></td><td>0.71<sup>+0.06</sup><sub>-0.06</sub></td><td>4300</td><td>19.8<sup>+0.1</sup><sub>-0.2</sub></td></tr><tr><td>GW200115_042309</td><td>7.4<sup>+1.7</sup><sub>-1.7</sub></td><td>2.43<sup>+0.05</sup><sub>-0.07</sub></td><td>5.9<sup>+2.0</sup><sub>-2.5</sub></td><td>1.44<sup>+0.85</sup><sub>-0.28</sub></td><td>-0.15<sup>+0.23</sup><sub>-0.42</sub></td><td>0.29<sup>+0.15</sup><sub>-0.10</sub></td><td>0.06<sup>+0.03</sup><sub>-0.02</sub></td><td>7.2<sup>+1.8</sup><sub>-1.7</sub></td><td>0.42<sup>+0.09</sup><sub>-0.04</sub></td><td>720</td><td>11.3<sup>+0.3</sup><sub>-0.5</sub></td></tr><tr><td>GW200128_022011</td><td>75<sup>+17</sup><sub>-12</sub></td><td>32.0<sup>+7.5</sup><sub>-5.5</sub></td><td>42.2<sup>+11.6</sup><sub>-8.1</sub></td><td>32.6<sup>+9.5</sup><sub>-9.2</sub></td><td>0.12<sup>+0.24</sup><sub>-0.25</sub></td><td>3.4<sup>+2.1</sup><sub>-1.8</sub></td><td>0.56<sup>+0.28</sup><sub>-0.28</sub></td><td>71<sup>+16</sup><sub>-11</sub></td><td>0.74<sup>+0.10</sup><sub>-0.10</sub></td><td>2600</td><td>10.6<sup>+0.3</sup><sub>-0.4</sub></td></tr><tr><td>GW200129_065458</td><td>63.3<sup>+4.5</sup><sub>-3.4</sub></td><td>27.2<sup>+2.1</sup><sub>-2.3</sub></td><td>34.5<sup>+9.9</sup><sub>-3.1</sub></td><td>29.0<sup>+3.3</sup><sub>-9.3</sub></td><td>0.11<sup>+0.11</sup><sub>-0.16</sub></td><td>0.89<sup>+0.26</sup><sub>-0.37</sub></td><td>0.18<sup>+0.05</sup><sub>-0.07</sub></td><td>60.2<sup>+4.1</sup><sub>-3.2</sub></td><td>0.73<sup>+0.06</sup><sub>-0.05</sub></td><td>54</td><td>26.8<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>GW200202_154313</td><td>17.58<sup>+1.78</sup><sub>-0.67</sub></td><td>7.49<sup>+0.24</sup><sub>-0.20</sub></td><td>10.1<sup>+3.5</sup><sub>-1.4</sub></td><td>7.3<sup>+1.1</sup><sub>-1.7</sub></td><td>0.04<sup>+0.13</sup><sub>-0.06</sub></td><td>0.41<sup>+0.15</sup><sub>-0.16</sub></td><td>0.09<sup>+0.03</sup><sub>-0.03</sub></td><td>16.76<sup>+1.87</sup><sub>-0.66</sub></td><td>0.69<sup>+0.03</sup><sub>-0.04</sub></td><td>160</td><td>10.8<sup>+0.2</sup><sub>-0.4</sub></td></tr><tr><td>GW200208_130117</td><td>65.3<sup>+8.1</sup><sub>-6.8</sub></td><td>27.7<sup>+3.7</sup><sub>-3.1</sub></td><td>37.7<sup>+9.3</sup><sub>-6.2</sub></td><td>27.4<sup>+6.3</sup><sub>-7.3</sub></td><td>-0.07<sup>+0.21</sup><sub>-0.27</sub></td><td>2.23<sup>+1.02</sup><sub>-0.85</sub></td><td>0.40<sup>+0.15</sup><sub>-0.14</sub></td><td>62.5<sup>+7.5</sup><sub>-6.4</sub></td><td>0.66<sup>+0.09</sup><sub>-0.12</sub></td><td>48</td><td>10.8<sup>+0.3</sup><sub>-0.4</sub></td></tr><tr><td>GW200208_222617</td><td>63<sup>+100</sup><sub>-26</sub></td><td>19.8<sup>+10.5</sup><sub>-5.2</sub></td><td>51<sup>+103</sup><sub>-30</sub></td><td>12.3<sup>+9.2</sup><sub>-5.5</sub></td><td>0.45<sup>+0.42</sup><sub>-0.46</sub></td><td>4.1<sup>+4.4</sup><sub>-2.0</sub></td><td>0.66<sup>+0.53</sup><sub>-0.29</sub></td><td>61<sup>+99</sup><sub>-26</sub></td><td>0.83<sup>+0.14</sup><sub>-0.26</sub></td><td>1900</td><td>7.4<sup>+1.4</sup><sub>-1.2</sub></td></tr><tr><td>GW200209_085452</td><td>62.6<sup>+13.9</sup><sub>-9.4</sub></td><td>26.7<sup>+6.0</sup><sub>-4.2</sub></td><td>35.6<sup>+10.5</sup><sub>-6.8</sub></td><td>27.1<sup>+7.8</sup><sub>-7.8</sub></td><td>-0.12<sup>+0.24</sup><sub>-0.30</sub></td><td>3.4<sup>+1.9</sup><sub>-1.8</sub></td><td>0.57<sup>+0.25</sup><sub>-0.26</sub></td><td>59.9<sup>+13.1</sup><sub>-8.9</sub></td><td>0.66<sup>+0.10</sup><sub>-0.12</sub></td><td>730</td><td>9.6<sup>+0.4</sup><sub>-0.5</sub></td></tr><tr><td>GW200210_092254</td><td>27.0<sup>+7.1</sup><sub>-4.3</sub></td><td>6.56<sup>+0.38</sup><sub>-0.40</sub></td><td>24.1<sup>+7.5</sup><sub>-4.6</sub></td><td>2.83<sup>+0.47</sup><sub>-0.42</sub></td><td>0.02<sup>+0.22</sup><sub>-0.21</sub></td><td>0.94<sup>+0.43</sup><sub>-0.34</sub></td><td>0.19<sup>+0.08</sup><sub>-0.06</sub></td><td>26.7<sup>+7.2</sup><sub>-4.3</sub></td><td>0.34<sup>+0.13</sup><sub>-0.08</sub></td><td>1800</td><td>8.4<sup>+0.5</sup><sub>-0.7</sub></td></tr><tr><td>GW200216_220804</td><td>81<sup>+20</sup><sub>-14</sub></td><td>32.9<sup>+9.3</sup><sub>-8.5</sub></td><td>51<sup>+22</sup><sub>-13</sub></td><td>30<sup>+14</sup><sub>-16</sub></td><td>0.10<sup>+0.34</sup><sub>-0.36</sub></td><td>3.8<sup>+3.0</sup><sub>-2.0</sub></td><td>0.63<sup>+0.37</sup><sub>-0.29</sub></td><td>78<sup>+19</sup><sub>-13</sub></td><td>0.70<sup>+0.14</sup><sub>-0.24</sub></td><td>2900</td><td>8.1<sup>+0.4</sup><sub>-0.5</sub></td></tr><tr><td>GW200219_094415</td><td>65.0<sup>+12.6</sup><sub>-8.2</sub></td><td>27.6<sup>+5.6</sup><sub>-3.8</sub></td><td>37.5<sup>+10.1</sup><sub>-6.9</sub></td><td>27.9<sup>+7.4</sup><sub>-8.4</sub></td><td>-0.08<sup>+0.23</sup><sub>-0.29</sub></td><td>3.4<sup>+1.7</sup><sub>-1.5</sub></td><td>0.57<sup>+0.22</sup><sub>-0.22</sub></td><td>62.2<sup>+11.7</sup><sub>-7.8</sub></td><td>0.66<sup>+0.10</sup><sub>-0.13</sub></td><td>700</td><td>10.7<sup>+0.3</sup><sub>-0.5</sub></td></tr><tr><td>GW200220_061928</td><td>148<sup>+55</sup><sub>-33</sub></td><td>62<sup>+23</sup><sub>-15</sub></td><td>87<sup>+40</sup><sub>-23</sub></td><td>61<sup>+26</sup><sub>-25</sub></td><td>0.06<sup>+0.40</sup><sub>-0.38</sub></td><td>6.0<sup>+4.8</sup><sub>-3.1</sub></td><td>0.90<sup>+0.55</sup><sub>-0.40</sub></td><td>141<sup>+51</sup><sub>-31</sub></td><td>0.71<sup>+0.15</sup><sub>-0.17</sub></td><td>3000</td><td>7.2<sup>+0.4</sup><sub>-0.7</sub></td></tr><tr><td>GW200220_124850</td><td>67<sup>+17</sup><sub>-12</sub></td><td>28.2<sup>+7.3</sup><sub>-5.1</sub></td><td>38.9<sup>+14.1</sup><sub>-8.6</sub></td><td>27.9<sup>+9.2</sup><sub>-9.0</sub></td><td>-0.07<sup>+0.27</sup><sub>-0.33</sub></td><td>4.0<sup>+2.8</sup><sub>-2.2</sub></td><td>0.66<sup>+0.36</sup><sub>-0.31</sub></td><td>64<sup>+16</sup><sub>-11</sub></td><td>0.67<sup>+0.11</sup><sub>-0.14</sub></td><td>3200</td><td>8.5<sup>+0.3</sup><sub>-0.5</sub></td></tr><tr><td>GW200224_222234</td><td>72.3<sup>+7.2</sup><sub>-5.3</sub></td><td>31.1<sup>+3.3</sup><sub>-2.7</sub></td><td>40.0<sup>+6.7</sup><sub>-4.5</sub></td><td>32.7<sup>+4.8</sup><sub>-7.2</sub></td><td>0.10<sup>+0.15</sup><sub>-0.16</sub></td><td>1.71<sup>+0.50</sup><sub>-0.65</sub></td><td>0.32<sup>+0.08</sup><sub>-0.11</sub></td><td>68.7<sup>+6.7</sup><sub>-4.8</sub></td><td>0.73<sup>+0.06</sup><sub>-0.07</sub></td><td>51</td><td>20.0<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>GW200225_060421</td><td>33.5<sup>+3.6</sup><sub>-3.0</sub></td><td>14.2<sup>+1.5</sup><sub>-1.4</sub></td><td>19.3<sup>+5.0</sup><sub>-3.0</sub></td><td>14.0<sup>+2.8</sup><sub>-3.5</sub></td><td>-0.12<sup>+0.17</sup><sub>-0.28</sub></td><td>1.15<sup>+0.51</sup><sub>-0.53</sub></td><td>0.22<sup>+0.09</sup><sub>-0.10</sub></td><td>32.1<sup>+3.5</sup><sub>-2.8</sub></td><td>0.66<sup>+0.07</sup><sub>-0.13</sub></td><td>370</td><td>12.5<sup>+0.3</sup><sub>-0.4</sub></td></tr><tr><td>GW200302_015811</td><td>57.8<sup>+9.6</sup><sub>-6.9</sub></td><td>23.4<sup>+4.7</sup><sub>-3.0</sub></td><td>37.8<sup>+8.7</sup><sub>-8.5</sub></td><td>20.0<sup>+8.1</sup><sub>-5.7</sub></td><td>0.01<sup>+0.25</sup><sub>-0.26</sub></td><td>1.48<sup>+1.02</sup><sub>-0.70</sub></td><td>0.28<sup>+0.16</sup><sub>-0.12</sub></td><td>55.5<sup>+8.9</sup><sub>-6.6</sub></td><td>0.66<sup>+0.13</sup><sub>-0.15</sub></td><td>6000</td><td>10.8<sup>+0.3</sup><sub>-0.4</sub></td></tr><tr><td>GW200306_093714</td><td>43.9<sup>+11.8</sup><sub>-7.5</sub></td><td>17.5<sup>+3.5</sup><sub>-3.0</sub></td><td>28.3<sup>+17.1</sup><sub>-7.7</sub></td><td>14.8<sup>+6.5</sup><sub>-6.4</sub></td><td>0.32<sup>+0.28</sup><sub>-0.46</sub></td><td>2.1<sup>+1.7</sup><sub>-1.1</sub></td><td>0.38<sup>+0.24</sup><sub>-0.18</sub></td><td>41.7<sup>+12.3</sup><sub>-6.9</sub></td><td>0.78<sup>+0.11</sup><sub>-0.26</sub></td><td>4600</td><td>7.8<sup>+0.4</sup><sub>-0.6</sub></td></tr><tr><td>GW200308_173609*</td><td>92<sup>+169</sup><sub>-48</sub></td><td>34<sup>+44</sup><sub>-18</sub></td><td>60<sup>+166</sup><sub>-29</sub></td><td>24<sup>+36</sup><sub>-13</sub></td><td>0.16<sup>+0.58</sup><sub>-0.49</sub></td><td>7.1<sup>+13.9</sup><sub>-4.4</sub></td><td>1.04<sup>+1.47</sup><sub>-0.57</sub></td><td>88<sup>+169</sup><sub>-47</sub></td><td>0.72<sup>+0.22</sup><sub>-0.35</sub></td><td>12 000</td><td>4.7<sup>+2.5</sup><sub>-2.9</sub></td></tr><tr><td>GW200311_115853</td><td>61.9<sup>+5.3</sup><sub>-4.2</sub></td><td>26.6<sup>+2.4</sup><sub>-2.0</sub></td><td>34.2<sup>+6.4</sup><sub>-3.8</sub></td><td>27.7<sup>+4.1</sup><sub>-5.9</sub></td><td>-0.02<sup>+0.16</sup><sub>-0.20</sub></td><td>1.17<sup>+0.28</sup><sub>-0.40</sub></td><td>0.23<sup>+0.05</sup><sub>-0.07</sub></td><td>59.0<sup>+4.8</sup><sub>-3.9</sub></td><td>0.69<sup>+0.07</sup><sub>-0.08</sub></td><td>35</td><td>17.8<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>GW200316_215756</td><td>21.2<sup>+7.2</sup><sub>-2.0</sub></td><td>8.75<sup>+0.62</sup><sub>-0.55</sub></td><td>13.1<sup>+10.2</sup><sub>-2.9</sub></td><td>7.8<sup>+2.0</sup><sub>-2.9</sub></td><td>0.13<sup>+0.27</sup><sub>-0.10</sub></td><td>1.12<sup>+0.48</sup><sub>-0.44</sub></td><td>0.22<sup>+0.08</sup><sub>-0.08</sub></td><td>20.2<sup>+7.4</sup><sub>-1.9</sub></td><td>0.70<sup>+0.04</sup><sub>-0.04</sub></td><td>190</td><td>10.3<sup>+0.4</sup><sub>-0.7</sub></td></tr><tr><td>GW200322_091133*</td><td>50<sup>+132</sup><sub>-22</sub></td><td>15.0<sup>+29.5</sup><sub>-4.0</sub></td><td>38<sup>+130</sup><sub>-22</sub></td><td>11.3<sup>+24.3</sup><sub>-6.0</sub></td><td>0.27<sup>+0.54</sup><sub>-0.58</sub></td><td>3.5<sup>+12.5</sup><sub>-2.2</sub></td><td>0.59<sup>+1.43</sup><sub>-0.32</sub></td><td>48<sup>+132</sup><sub>-22</sub></td><td>0.77<sup>+0.19</sup><sub>-0.39</sub></td><td>18 000</td><td>4.5<sup>+2.7</sup><sub>-3.0</sub></td></tr></tbody></table>
<figure><img src="image_10.png" /><figcaption>FIG. 7. Marginal probability distributions for the source chirp mass *M*, mass ratio *q*, effective inspiral spin $\chi_{\text{eff}}$, effective precession spin $\chi_p$, and luminosity distance $D_L$ for O3b candidates with $p_{\text{astro}} > 0.5$ plus GW200105_162426. The colored upper half of the plot shows the marginal posterior distributions, and the white lower half of the plot shows the marginal prior distributions. The vertical extent of each colored region is proportional to one-dimensional marginal probability distribution at a given parameter value for the corresponding candidate. We highlight with italics GW200105_162426 as it has $p_{\text{astro}} < 0.5$, as well as GW191219_163120 because of significant uncertainty in its $p_{\text{astro}}$ and because it has significant posterior support outside of mass ratios where the waveform models have been calibrated. Results for GW200308_173609 and GW200322_091133 include a low-likelihood mode at large distances and high masses. Colors correspond to the date of observation.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>FIG. 8. Credible-region contours for the inferred masses of the O3b candidates with $p_{astro} > 0.5$ plus GW200105_162426. Top: results for the primary and secondary component masses $m_1$ and $m_2$. The shaded areas indicate regions excluded by the convention $m_1 \ge m_2$, and by the most extreme mass ratio considered in our analyses (detailed in Appendix E 3). Bottom: results for total mass $M$ and mass ratio $q$. Each contour represents the 90% credible region for a different candidate. Highlighted contours are for the NSBH candidates GW191219_163120, GW200105_162426, and GW200115_042309; the NSBH or low-mass BBH candidate GW200210_092254; GW191204_171526, which has inferred $\chi_{eff} > 0$; GW200225_060421, which has 85% probability that $\chi_{eff} < 0$, and GW200220_061928, which probably has the most massive source of the O3b candidates. We highlight with italics GW200105_162426 as it has $p_{astro} < 0.5$, as well as GW191219_163120 because of significant uncertainty in its $p_{astro}$ and because it has significant posterior support outside of mass ratios where the waveform models have been calibrated. Results for GW200308_173609 and GW200322_091133 are indicated with dashed lines to highlight that these include a low-likelihood mode at large distances and high masses, and are particularly prior sensitive. The dotted lines delineate regions where the primary and secondary can have a mass below $3M_\odot$. For the region above the $m_2 = 3M_\odot$ line, both objects in the binary have masses above $3M_\odot$.</figcaption></figure>

Posterior samples are available from GWOSC [33], and the simple form of the prior probability distributions enables the samples to be conveniently reweighted to use alternative prior distributions [150,151]. Inferences about the underlying population of merging compact binaries are presented in a companion paper [5].

The O3b candidates show a diversity in their source properties. Many are similar to previous observations, but some do show unusual features. While the mass posterior probability distributions are typically unimodal, some results show multimodal behavior. For example,

GW200129_065458 shows a bimodality in mass ratio that translates to a bimodality in $m_2$. GW200225_060421 and GW200306_093714 both show bimodality in their redshifted chirp-mass distributions, although their source-mass distributions (shown in Fig. 7) are unimodal, as the additional uncertainty from the inferred redshift is sufficient to broaden the modes such that they merge. Because of the correlations between masses and spins [152–154], multimodality in mass distributions may also translate to multiple peaks in the effective inspiral spin distribution. Multimodality can arise due to the complexity of the
<figure><img src="image_12.png" /></figure>

FIG. 9. Credible-region contours in the plane of chirp mass $M$ and effective inspiral spin $\chi_{\text{eff}}$ for O3b candidates with $p_{\text{astro}} > 0.5$ plus GW200105_162426. Each contour represents the 90% credible region for a different candidate. Highlighted contours are for the NSBH candidates GW191219_163120, GW200105_162426, and GW200115_042309; the NSBH or low-mass BBH candidate GW200210_092254; GW191204_171526, which has inferred $\chi_{\text{eff}} > 0$; GW200225_060421, which has 85% probability that $\chi_{\text{eff}} < 0$, and GW200220_061928, which probably has the most massive source of the O3b candidates. We highlight with italics GW200105_162426 as it has $p_{\text{astro}} < 0.5$, as well as GW191219_163120 because of significant uncertainty in its $p_{\text{astro}}$ and because it has significant posterior support outside of mass ratios where the waveform models have been calibrated. Results for GW200308_173609 and GW200322_091133 are indicated with dashed lines to highlight that these include a low-likelihood mode at large distances and high masses, and are particularly prior sensitive.

likelihood surface when using waveform models that include higher-order multipole moments [19,155–157] and precession [158,159], noise fluctuations for quiet signals [160], the presence of glitches [161–163], or there being multiple overlapping signals in the data (which is unlikely given O3 sensitivity) [164]. Therefore, multimodality is expected in a few cases.

Cases with significant multimodality are GW200208_222617, GW200308_173609, and GW200322_091133. These candidates have modest significance with $p_{\text{astro}} = 0.70, 0.86$, and $0.62$, respectively, and are each identified with $p_{\text{astro}} > 0.5$ by only one search analysis. They have low SNRs, and using IMRPhenomXPHM they are inferred to have $\rho = 7.4_{-1.2}^{+1.4}$, $4.7_{-2.9}^{+2.5}$, and $4.5_{-3.0}^{+2.7}$, respectively. For GW200208_222617, the two main modes have comparable likelihoods, indicating comparable fits to the data, while for GW200308_173609 and GW200322_091133, there are significant modes with lower likelihoods. The posterior probability distributions for GW200308_173609 and GW200322_091133 both have peaks at lower masses and lower distances, and another broader peak corresponding to higher masses and larger distances; this high-mass, large-distance peak is dominated by the prior. The default prior probability distribution (described in Appendix E 3) places significant weight at large distances and at high masses. This means that we can find significant posterior probability at large distances and high masses, even when the likelihood is low. Such low-likelihood peaks, corresponding to low SNRs, may arise due to a random noise fluctuation matching the signal template.

For GW200308_173609 and GW200322_091133, the high-mass and high-distance peak has lower likelihood and posterior support for SNRs $\rho \sim 0$. For such candidates, the multimodality indicates that we cannot separate the possibility of a signal from a lower-mass, closer source from a weaker (potentially vanishing) signal from a higher-mass, more-distant source. However, this support for high masses and large distances is driven by our choice of prior, which is not designed to model the astrophysical population of sources. Therefore, we consider that the high-likelihood peaks for GW200308_173609 and GW200322_091133 yield a more plausible estimate of the source parameters, although we cannot exclude the possibility that the low-likelihood peaks describe the sources (assuming that the signals are astrophysical).

All results are given assuming our default priors. We highlight results for GW200308_173609 and GW200322_091133 in Table IV and the figures to indicate that these results may be especially sensitive to the choice of prior. Using a different prior, such as a population-informed prior [116,119,165–169], that has a stronger preference for masses more consistent with other GW observations, and a weaker preference for high masses and large distances, would alter results.

## A. Masses

Masses are typically the best constrained binary parameters. They are the dominant properties in setting the frequency evolution of the signal, with lower- (higher-) mass systems merging at higher (lower) frequencies.
While we are typically interested in the source masses, it is the redshifted masses $(1+z)m_i$, where $z$ is the source redshift, that are measured by the detectors [101]. The source masses are calculated by combining the inferred redshifted mass and luminosity distance (see Appendix E for the assumed cosmology).

Combinations of the two component masses (such as the chirp mass) may be more precisely measured than the individual component masses [152–154,170]. However, component masses are most informative about the nature of the source, and indicate whether the compact object is more likely to be a BH or a NS. The maximum NS mass is currently uncertain, with estimates ranging over $2.1–2.7 M_\odot$ [171–176]. We use $3M_\odot$ as a robust upper limit of the maximum NS mass [9,10], and split the candidates into two categories: unambiguous BBHs where, assuming that the signal is astrophysical, both components of the source were BHs ($m_2 > 3M_\odot$ at 99% probability), and potential-NS binaries (in our case, potential-NSBH binaries) where at least one component could have been a NS. Candidates from the two categories are discussed in Secs. VA 1 and VA 2, respectively. As shown in Fig. 8, all of the 35 candidates with $p_{astro} > 0.5$ except GW191219_163120, GW200115_042309, and GW200210_092254 (plus GW200105_162426) have $m_2 > 3M_\odot$, and none of the candidates have posterior support for $m_1 < 3M_\odot$, which would be required for a BNS source. Therefore, we identify the majority of sources as BBHs.

# 1. *Masses of sources with strictly* $m_2 > 3M_\odot$: *Unambiguous BBHs*

The mass combination with greatest influence on a CBC signal's frequency evolution is the chirp mass $M$ [98]. The chirp mass's influence on the inspiral means that it is more precisely measured in lower-mass systems, which have more of the inspiral signal in the sensitive frequency band of the detectors [177–181]. This is illustrated in Fig. 9, which also shows the effective inspiral spin (Sec. V B). The modestly significant ($p_{astro} = 0.62$) GW200220_061928 probably has the highest chirp-mass source of the O3b candidates, with $M = 62_{-15}^{+23} M_\odot$. Similarly, GW191129_134029's source probably has the lowest while still being an unambiguous-BBH ($m_2 > 3M_\odot$) candidate, with $M = 7.31_{-0.28}^{+0.43} M_\odot$. The range of chirp masses for the O3b candidates is consistent with GWTC-2.1 [3,4].

The total mass of the binary $M$ influences the merger and ringdown of the signal, which constitute a more significant proportion of the observed signal for higher-mass sources [13,182,183]. The O3b candidates with the highest $M$ measurements, GW200220_061928 and (the multimodal) GW200308_173609, have lower median $M$ measurements than GW190521 [4,184], of $M = 148_{-33}^{+55} M_\odot$ and $92_{-48}^{+169} M_\odot$, respectively. The lowest-mass O3b unambiguous-BBH candidate is GW191129_134029's source, with

$M = 17.5_{-1.2}^{+2.4} M_\odot$. Posterior probability distributions for the total mass and mass ratio are shown in Fig. 8; the curving degeneracies seen at lower masses are where distributions follow a line of constant chirp mass.

Mass ratios are typically less precisely inferred from GW observations than the chirp mass or total mass. The mass ratio influences the phase evolution of the inspiral at the post-Newtonian (PN) order after the chirp mass [98,135,152,153]. Most measured mass ratios are consistent with the equal-mass limit $q = 1$, as shown in Fig. 7. For example, GW200129_065458 and GW200311_115853 have $q \ge 0.50$ and $\ge 0.61$ at 90% probability, respectively. However, multiple BBH candidates have support for unequal masses. GW191113_071753's source has an inferred $q = 0.202_{-0.087}^{+0.490}$ ($q \le 0.524$ at 90% probability) and GW200208_222617's source has $q = 0.21_{-0.16}^{+0.67}$ ($q \le 0.79$ at 90% probability). Some posterior probability distributions extend outside the calibration range for current waveform models, and hence may be subject to additional systematic uncertainties [136,137]. Future analysis with waveforms with improved fidelity at more extreme mass ratios should lead to a more complete understanding of these sources. GW191113_071753 and GW200208_222617 have moderate significance ($p_{astro} = 0.68$ and 0.70, respectively), and hence may not be a reflection of the true BBH population. Using a population-informed prior [116,119,165–169], in place of our default uninformative prior, may give greater weight to equal masses [5].

Considering individual BH masses, the unambiguous-BBH candidates have component masses ranging from approximately $5.9_{-1.3}^{+4.4} M_\odot$ to approximately $87_{-23}^{+40} M_\odot$. Primary masses range from $10.1_{-1.4}^{+3.5} M_\odot$ for GW200202_154313 to $87_{-23}^{+40} M_\odot$ and $60_{-29}^{+166} M_\odot$ for GW200220_061928 and GW200308_173609, while secondary masses range from $5.9_{-1.3}^{+4.4} M_\odot$ for GW191113_071753 to $61_{-25}^{+26} M_\odot$ for GW200220_061928. The distribution of component masses is analyzed and its astrophysical implications discussed in a companion paper [5].

Given our default prior assumptions, there is a 94% probability that the primary BH in GW200220_061928 has a mass $m_1 > 65 M_\odot$; this is approximately the maximum mass of BHs expected to be formed from stellar collapse before encountering pair-instability supernovae [156,185–190], where the progenitor stars would be disrupted leaving no remnant behind, although there are many physical uncertainties that can impact this maximum mass [191–198]. GW191109_010717 has 51% probability that $m_1 > 65 M_\odot$, while GW200208_222617 and GW191127_050227 have probabilities 42% and 30%, respectively. Similarly, GW200220_061928 has a 39% probability that its secondary has $m_2 > 65 M_\odot$. GW200220_061928 and GW200208_222617 have 7% and 6% probabilities that $m_1 > 120 M_\odot$, respectively, which
is expected to be approximately the mass where the pair-instability supernova mass gap ends [156,189,194,199,200].

Based upon x-ray binary observations, there is a hypoth-
esized lower BH mass gap below $5M_{\odot}$ [201–204]. This
may be a signature of the physics of core-collapse super-
nova explosions [205–209]. We infer that there are some
BBHs that may have components in this mass gap. Given
our standard prior assumptions, the candidate with the most
posterior support for $m_2 < 5M_{\odot}$ is GW19113_071753
with 13% probability. None of the unambiguous-BBH
candidates has a primary mass consistent with being in
the lower mass gap.

The component BH masses overlap with those from
previous GW and electromagnetic observations. The range
is consistent with observations in GWTC-2.1 [4,184].
Non-LVK analysis of public GW data has led to other
BBH candidates being reported [15–19,210]; these BBHs
have inferred masses and mass ratios that are consistent
with the systems found here. From these non-LVK
searches, the marginal candidate GW170817A [18,211]
may have the most massive source, with $m_1 = 56_{-10}^{+16}M_{\odot}$
and $m_2 = 40_{-11}^{+10}M_{\odot}$. While overlapping at lower masses, the
BH masses inferred from GW observations extend above the
masses seen in x-ray binaries [202,203,212–215]. However,
these x-ray binaries are largely expected not to form merging
BBHs [216,217]: For example, while Cygnus X-1 may form
two BHs, predictions indicate that there is only a small
probability that they would merge within a Hubble time
[218]. Additionally, x-ray observations are typically drawn
from binaries with near solar metallicity. Stellar mass loss
due to winds increases with metallicity [219–221], so stars
formed at solar metallicity leave less massive remnants than
stars formed at lower metallicity with the same initial mass
[189,222–226]. Studying the masses of BHs will pro-
vide insight into their formation and the lives of their
progenitors [199,227–234].

The remnant BHs formed from the mergers have masses $M_f = M - E_{\text{rad}}/c^2$ where $E_{\text{rad}}$ is the energy radiated as GWs, which typically corresponds to a few percent of $M$ [235–238]. The most massive remnant BH among the O3b candidates probably corresponds to GW200220_061928, with a final mass of $141_{-31}^{+51}M_{\odot}$. Using our default priors, there is a 99% probability of its final BH mass being above $100M_{\odot}$ (a conventional threshold for being considered an IMBH [26,239,240]). Several other systems are consistent with $M_f > 100M_{\odot}$, including GW191109_010717's remnant, which has a 78% probability of exceeding this threshold.

## 2. Masses of sources with support for $m_2 < 3M_{\odot}$: Potential-NS binaries

The candidates GW191219_163120, GW200115_042309, GW200210_092254, and GW200105_162426 are all consistent with originating from a source with $m_2 < 3M_{\odot}$. When a coalescing binary contains a NS,

matter effects modify the waveform. If these effects can
be measured, we can identify that the component is a NS
rather than a BH. For O3b candidates, as discussed in
Sec. V C, we find no measurable matter effects. Without
this information, from the GW signal we can infer only the
component type from their masses.

As illustrated by Figs. 7 and 8, the O3b candidates with potential-NS binary sources have more extreme mass ratios than the typical BBH candidates. At 90% probability, the sources of GW191219_163120, GW200105_162426, GW200115_042309, and GW200210_092254 have mass ratios $q \le 0.041$, $\le 0.258$, $\le 0.571$, and $\le 0.150$, respectively. The mass ratio of GW200210_092254's source is $q = 0.118_{-0.041}^{+0.048}$, which is comparable to GW190814's $q = 0.11_{-0.01}^{+0.01}$ [4,241]. The mass ratio of GW191219_163120's source is inferred to be $0.038_{-0.004}^{+0.005}$, which is extremely challenging for waveform modeling, and thus, there may be systematic uncertainties in results for this candidate.

GW200115_042309's source is the lowest total mass O3b binary; this potential NSBH coalescence has $M = 7.4_{-1.7}^{+1.7}M_{\odot}$. Its chirp mass is well measured at $M = 2.43_{-0.07}^{+0.05}M_{\odot}$. GW200115_042309's source has components with masses $m_1 = 5.9_{-2.5}^{+2.0}M_{\odot}$ and $m_2 = 1.44_{-0.28}^{+0.85}M_{\odot}$. These results are consistent with previous inferences [8], showing that the change in how the fast scattering glitches in Livingston data were mitigated (discussed in Appendix C) does not have a significant impact on this analysis. The primary is consistent with being a low-mass BH [8], and we infer a 29% probability that $m_1 < 5M_{\odot}$; the secondary is consistent with the masses of known Galactic NSs [173,242–244].

GW200105_162426's source corresponds to a higher-
mass NSBH candidate, with $M = 11.0_{-1.4}^{+1.5}M_{\odot}$ and
$M = 3.42_{-0.08}^{+0.08}M_{\odot}$. The binary components have masses
$m_1 = 9.1_{-1.7}^{+1.7}M_{\odot}$ and $m_2 = 1.91_{-0.24}^{+0.33}M_{\odot}$, which are con-
sistent with a BH and a NS, respectively [8].

GW200210_092254's source has $M = 27.0_{-4.3}^{+7.1}M_{\odot}$ and $M = 6.56_{-0.40}^{+0.38}M_{\odot}$, which sit within the range seen for the unambiguous-BBHs candidates discussed in Sec. VA 1. While the primary is clearly a BH with $m_1 = 24.1_{-4.6}^{+7.5}M_{\odot}$, its secondary has $m_2 = 2.83_{-0.42}^{+0.47}M_{\odot}$ with a 76% probability that $m_2 < 3M_{\odot}$. The secondary mass sits within the hypothesized lower mass gap between NSs and BHs [201–204]. The inferred $m_2$ is comparable to (i) the $3.3_{-0.7}^{+2.8}M_{\odot}$ (95% confidence) candidate BH in the non-interacting binary 2MASS J05215658+4359220 [245], (ii) the $3.04 \pm 0.06M_{\odot}$ (68% confidence) candidate BH binary companion to V723 Mon [246], although this binary has alternatively been interpreted as a stripped low-mass giant star with a subgiant companion [247], and (iii) potentially the pulsar J1748–2021B's estimated mass of $2.74 \pm 0.21M_{\odot}$ (68% confidence) if the assumption of purely relativistic precession (with no contributions from tidal or rotational distortion of the
companion) is accurate [248]. GW200210_092254's source is similar to GW190814's, where the component masses were inferred to be $m_1 = 23.3_{-1.4}^{+1.4} M_\odot$ and $m_2 = 2.6_{-0.1}^{+0.1} M_\odot$ [4,241]. GW200210_092254's source could either be a BBH or a NSBH system, but given the current understanding of the maximum NS mass [173,174,249–254], it is more probable that it is a BBH, similar to the case for GW190814 [241].

For GW191219_163120, we infer a source with $M = 32.3_{-2.7}^{+2.2} M_\odot$ and $M = 4.31_{-0.17}^{+0.12} M_\odot$. It has $m_1 = 31.1_{-2.8}^{+2.2} M_\odot$ and $m_2 = 1.17_{-0.06}^{+0.07} M_\odot$, which would make the source a clear NSBH, assuming that the signal is astrophysical. The secondary is probably the least massive compact object among the O3b observations, and is comparable to the least massive of known NSs [173,242,255]: for example, the companion to pulsar J0453+1559 that has an estimated mass of $1.174 \pm 0.004 M_\odot$ (68% confidence) [256], although this object has also been suggested to be a white dwarf [257]; the pulsar J1802–2124 that has an estimated mass $1.24 \pm 0.11 M_\odot$ (68% confidence) [258], or the NSs in the high-mass x-ray binaries SMC X-1 and 4U 1538–522 that have inferred masses of $1.21 \pm 0.12 M_\odot$ and $1.02 \pm 0.17 M_\odot$ (68% confidence), respectively [259].

Measuring the mass distribution of NSs will illuminate the physical processes that form them. Determining the maximum NS mass provides a key insight into the properties of NS matter [250,253,254,260–264], while determining the spectrum of NS masses provides an insight into the physics of processes such as supernova explosions [209,257,265–270]. As the catalog of observations grows, it will be possible to better determine the NS mass distribution.

## B. Spins

Spins leave a relatively subtle imprint on the GW signal, and so they are more difficult to measure from observations than the masses [13,152–154,170,271–273]. Typically, it is not possible to put strong constraints on individual components' spins, as the evolution of the system is primarily determined by mass-weighted combinations of the two component spins [274–278]. However, when a binary has unequal masses it may also be possible to constrain the primary spin because $\chi_1$ dominates the spin contributions to the signal. To reflect how the two spins influence the signal, we quote results for two convenient spin parameters: the effective inspiral spin $\chi_{\text{eff}}$ [99,100] and the effective precession spin $\chi_p$ [279,280].

The effective inspiral spin, as defined in Eq. (2), describes the mass-weighted projection of the component spins parallel to the orbital angular momentum, and is approximately conserved throughout the inspiral [281] while remaining important in determining evolution through the merger [236,282,283]. The effective inspiral spin influences the length of the inspiral and the transition

to merger [236,275,282,284]. A nonzero $\chi_{\text{eff}}$ indicates the definite presence of spins in the system, with positive values indicating that there is a net spin aligned with the orbital angular momentum, and negative values indicating that there is a net spin antialigned with the orbital angular momentum.

The effective precession spin,

$$ \chi_p = \max \left\{ \chi_{1,\perp}, \frac{q(4q+3)}{4+3q} \chi_{2,\perp} \right\}, \quad (4) $$

where $\chi_{i,\perp}$ is the component of spin perpendicular to the direction of the Newtonian orbital angular momentum $\hat{L}_N$, measures the mass-weighted in-plane spin component that contributes to spin precession [279,280,285,286]. With this parametrization, a value of $\chi_p = 0$ would indicate no spin precession, and a value of $\chi_p = 1$ indicates maximal precession; typically, only weak constraints are placed on $\chi_p$, so the posterior covers a significant fraction of its prior range [3,287,288]. Since $\chi_p$ is weakly constrained, the shape of the $\chi_p$ prior often dominates the posterior. The $\chi_p$ prior tends to zero at $\chi_p = 0$ and peaks at a moderate value of $\chi_p$ that depends on the prior ranges of $\chi_1, \chi_2$, and $q$, and so an inferred nonzero value does not necessarily imply a measurement of precession.

As a consequence of orbital precession, $\chi_p$ changes throughout the inspiral. However, the tilt angles of a compact binary at a formally infinite separation are well defined [289]. We thus quote the tilt angles and the derived quantities ($\chi_{\text{eff}}$ and $\chi_p$) at a fiducial reference point of infinite separation. The spins are evolved to infinite separation [290] using precession-averaged evolution [289,291] with the orbital angular momentum calculated using higher-order PN expressions.

The spin orientations of a binary can provide clues to its formation channel [149,232,292–296]. Dynamically assembled binaries would have no preferred spin orientation, and therefore are expected to have an isotropic distribution of spin orientations (unless embedded in an environment like the disk of an active galactic nucleus where accretion or consecutive mergers can result in an anisotropic spin distribution [297–301]); on the other hand, binaries formed through isolated binary evolution are typically expected to have nearly aligned spins, with moderate misalignments arising due to supernova kicks [302–308]. Therefore, negative $\chi_{\text{eff}}$ or large $\chi_p$ would be more common in dynamically formed binaries than those formed through isolated evolution.

Most of the candidates in O3b are consistent with $\chi_{\text{eff}} = 0$. However, GW191204_171526's source has $\chi_{\text{eff}} = 0.16_{+0.08}^{+0.05}$ with no posterior support at zero, while GW191103_012549, GW191126_115259, and GW191216_213338 have sources with $\chi_{\text{eff}} = 0.21_{-0.10}^{+0.16}$, $0.21_{-0.11}^{+0.15}$, and $0.11_{-0.06}^{+0.13}$, respectively, and negligible support for $\chi_{\text{eff}} < 0$.
Other candidates with significant support for $\chi_{\text{eff}} > 0$ include GW200316_215756, GW200208_222617, GW191129_134029, and GW200129_065458 with $\chi_{\text{eff}} > 0$ at 98%, 95%, 91%, and 89% probability, respectively. The O3b candidates with the most significant support for $\chi_{\text{eff}} < 0$ are GW191109_010717 and GW200225_060421 with $\chi_{\text{eff}} < 0$ at 90% and 85% probability, respectively. As with previous catalogs, there are more systems with $\chi_{\text{eff}} > 0$ than with $\chi_{\text{eff}} < 0$ [3,4,116,211].

Figure 7 shows one-dimensional posterior probability distributions for $\chi_{\text{eff}}$ and $\chi_p$, and Fig. 9 shows two-dimensional posterior probability distributions for $M$ and $\chi_{\text{eff}}$. GW200208_222617 has a high inferred value of $\chi_{\text{eff}} = 0.45_{-0.46}^{+0.42}$. This value is comparable to that inferred for GW190403_051519 ($p_{\text{astro}} = 0.60$, as given in Table XV in Appendix D 7), which has $\chi_{\text{eff}} = 0.68_{-0.43}^{+0.16}$ [4]. Both of these modest-significance candidates correspond to BBHs that have support for unequal masses. For example, GW190403_051519's source has $q = 0.23_{-0.12}^{+0.57}$. The O3b source with probably the lowest $\chi_{\text{eff}}$ is GW191109_010717's, which has $\chi_{\text{eff}} = -0.29_{-0.31}^{+0.42}$. Overall, the range of inferred $\chi_{\text{eff}}$ values matches the range for previous LVK candidates [4] as well as candidates from non-LVK analyses (when adopting comparable prior assumptions) [17,19,309,310].

The in-plane spin components are less well constrained than those parallel to the orbital angular momentum. Given the constraint that spin magnitudes cannot exceed 1, a measurement of $\chi_{\text{eff}}$ influences the permitted values of $\chi_p$. This constraint means that the $\chi_p$ posterior probability distribution may appear different from its (unrestricted) prior distribution even in cases where the signal contains no measurable information on the in-plane spins [14,288]. Figure 10 shows the $\chi_p$ posterior probability distribution compared to the prior distribution after conditioning on the $\chi_{\text{eff}}$ measurement for a selection of candidates [3]. These distributions would be the same if no information about the in-plane spin components had been extracted from the signal, and the selected candidates have the greatest difference between the two distributions. For many candidates, the $\chi_p$ posteriors are broad and uninformative. GW200129_065458 (the highest SNR O3b candidate) has probably the highest inferred $\chi_p$ of $0.52_{-0.38}^{+0.41}$. However, this inference is sensitive to the waveform model used, and is discussed in Sec. V E. GW191219_163120 has probably the lowest measurement of the O3b candidates, with $\chi_p \le 0.14$ at 90% probability, which is between the measurements for GW200105_162426 [8] and GW190814 [4,241] of $\chi_p \le 0.19$ and $\le 0.07$ at 90% probability, respectively. Since the mass ratio for this system is beyond the region of calibration for the waveforms, it is not clear how reliable this result is, and further work is needed to characterize the spin. For unequal-mass binaries, it is generally easier to observe the effects of

<figure><img src="image_13.png" /><figcaption>FIG. 10. Posterior (left; colored) and effective prior (right; white) probability distributions for the effective precession spin parameter $\chi_p$ of selected candidates. For each candidate, the prior distribution is conditioned on the posterior probability distribution for the effective inspiral spin $\chi_{\text{eff}}$ to illustrate how measurement of this quantity is correlated with inference of $\chi_p$. Horizontal lines mark the median and symmetric 90% interval for the distributions. The candidates selected show the greatest difference between the effective prior and posterior distributions. We highlight with italics GW200105_162426 as it has $p_{\text{astro}} < 0.5$, as well as GW191219_163120 because of significant uncertainty in its $p_{\text{astro}}$ and because it has significant posterior support outside of mass ratios where the waveform models are calibrated.</figcaption></figure>

precession (or lack thereof), enabling tighter constraints on $\chi_p$ [241,273,285,288].

Figure 11 shows the posterior probability distributions for the dimensionless spin magnitude $\chi_i$ and tilt angle $\theta_{LS_i}$ for the binary components of a selection of six O3b candidates. In most cases, posteriors for the component spin magnitudes are largely uninformative, but for some of the unequal-mass binaries we may constrain $\chi_1$ [241,278,311,312]. For GW191219_163120, GW200105_162426, and GW200210_092254, we find $\chi_1 \le 0.15$, $\le 0.26$, and $\le 0.38$ at 90% probability, respectively. Like GW190814 [4,241], where we inferred $\chi_1 \le 0.08$, these NSBHs or BBHs with low-mass secondaries have negligible support for maximal primary spins. Conversely, for the asymmetric BBH candidate GW200208_222617, we infer $\chi_1 \ge 0.30$ at 90% probability, with 51% probability that $\chi_1 > 0.8$. These inferred spins are not as extreme as they are for GW190403_051519's source [4]. With our default prior assumptions, only the O3a candidates GW190403_051519 [4], GW190412 [278,311], and GW190517_055101 [4] lack posterior support for a primary spin of zero.
<figure><img src="image_14.png" /><figcaption>FIG. 11. Posterior probability distributions for the dimensionless component spins $\vec{\chi}_1 = c\vec{S}_1/(Gm_1^2)$ and $\vec{\chi}_2 = c\vec{S}_2/(Gm_2^2)$ relative to the orbital plane, marginalized over azimuthal angles, for candidates GW191103_012549, GW191109_010717, GW191204_171526, GW191219_163120, GW200129_065458, and GW200210_092254, ordered chronologically. BBH waveform models are used for all the results shown here. GW191103_012549 has $\chi_{\text{eff}} = 0.21_{-0.10}^{+0.16}$ with negligible posterior support at zero. GW191109_010717 has $\chi_{\text{eff}} < 0$ at 90% probability and $\chi_p = 0.63_{-0.38}^{+0.28}$. GW191204_171526 has $\chi_{\text{eff}} = 0.16_{-0.05}^{+0.08}$ with no posterior support at zero. GW191219_163120 is a NSBH candidate with $\chi_p \le 0.14$ at 90% probability; this candidate has significant uncertainty in its $p_{\text{astro}}$ and has significant posterior support outside of mass ratios where the waveform models are calibrated. GW200129_065458 has $\chi_p = 0.52_{-0.38}^{+0.41}$. GW200210_092254 has $\chi_p \le 0.32$ at 90% probability and mass ratio $q = 0.118_{-0.041}^{+0.048}$. In these plots, histogram bins are constructed linearly in spin magnitude and the cosine of the tilt angles such that they contain equal prior probability.</figcaption></figure>

The final spin of the merger remnant $\chi_f$ is determined by conservation of angular momentum, and receives contributions from both the orbital angular momentum at merger and the component spins. For equal-mass, nonspinning BHs, the merger remnant has a spin of $\chi_f \sim 0.7$ [313–316]. As a consequence of the range of mass ratios and spins of the O3b candidates, there is a range of final spins from $\chi_f = 0.14_{-0.06}^{+0.06}$ for GW191219_163120 and $0.34_{-0.08}^{+0.13}$ for GW200210_092254 (assuming the BBH waveform models are accurate) to $0.83_{-0.26}^{+0.14}$ for GW200208_222617.

In comparison to GWTC-3 observations, spins of BHs in x-ray binaries span the full range of magnitudes, including near-maximal spins [215,317,318]. For low-mass x-ray binaries, it is possible that these spins are grown by accretion from their companion [319–321]; in contrast, for high-mass x-ray binaries there would be insufficient time for accretion to significantly change the spin [215,322,323]. The comparison between spins in x-ray binaries and coalescing BH binaries may highlight details of their formation and differences in their evolution.

Predictions for BH spin magnitudes vary, depending upon the formation channel and assumptions about stellar evolution such as stellar winds or the efficiency of stellar tides [193,230,306,324–326]. If angular momentum transport is efficient in stars, then BHs formed from stellar collapse may be born with low ($\lesssim 0.1$) spins [327,328]; for binaries formed via isolated binary evolution, this may mean that the first-born BH is expected to have a low spin, although the second-born BH may have a larger spin due to tides spinning up its progenitor [329–331]. The situation may be different if progenitor stars have significant rotation rates, such as for close binary star systems, where tidal locking can lead to chemically homogeneous evolution [332–334]. In this case, predicted BH spins are typically approximately 0.3–0.5, and may extend up to the Kerr limit [232,335]. Spin could also be imparted by asymmetric supernova explosions [307]. For BBHs embedded in active galactic nuclei disks, accretion can grow spins if they are prograde with respect to the disk, while retrograde spins become smaller before flipping to become prograde,
with the rate of evolution depending upon the orientation of the orbit with respect to the disk [297,300,301]. Outside of stellar evolution, primordial BHs born in the early, radiation-dominated Universe are expected to have small ($\lesssim 0.01$) spins at formation [336–338], but spins could increase through accretion [339,340]. Given the theoretical uncertainties on BH spin magnitudes, GW (and x-ray) observations may reveal details of BH formation; the distribution of spins is analyzed in a companion paper [5].

### C. Tidal effects

If a binary contains at least one NS component, the GW signal from the inspiral is influenced by the deformability of NS matter. Tidal effects are quantified by the dimensionless quadrupole tidal deformability,

$$ \Lambda_i = \frac{2}{3} k_{2,i} \left[ \frac{c^2 R_i}{Gm_i} \right]^5, \qquad (5) $$

where $k_{2,i}$ is the second Love number and $R_i$ is the component's radius [341,342]. Quasiuniversal relations [343] are used to parametrize the effects of NS spin-induced deformations in terms of $\Lambda_i$. Stiffer NS equations of state give larger values of $\Lambda_i$, which accelerates the rate of inspiral. BHs have $\Lambda_i = 0$ [344–347].

On account of their SNRs, we do not expect to be able to place a lower limit on the tidal deformability for any candidates from O3b [348–350]. Results confirm this, with no analysis showing strong support for matter effects. This is consistent with previous observations where it was not possible to determine the nature of the compact objects from the GW data alone, such as GW170817 [126,260] and GW190814 [241].

### D. Localization

The distance to the source is inferred from the amplitude of the signal as the two are inversely related [131,135]. Posterior probability distributions for the luminosity distance are shown in Fig. 7. The closest source found in O3b is probably GW200105_162426, with an inferred distance of $D_L = 0.27_{-0.11}^{+0.12}$ Gpc and redshift $z = 0.06_{-0.02}^{+0.02}$. At 90% probability, GW200105_162426 has $D_L \le 0.36$ Gpc. GW200308_173609 probably has the farthest source (including the high-distance, low-likelihood mode) at $D_L = 7.1_{-4.4}^{+13.9}$ Gpc ($D_L \ge 3.5$ Gpc at 90% probability), $z = 1.04_{-0.57}^{+1.47}$. This measurement is comparable to the probably most distant source reported in GWTC-2.1, which is for GW190403_051519 at $D_L = 8.28_{-4.29}^{+6.72}$ [3,4]. As our detectors become more sensitive, it will be possible to observe sources at greater distances.

The sky localization depends critically upon the number of observatories able to detect a signal [25,351,352]. With only a single detector observing, localizations may cover the entire sky. The most constrained localizations are

achieved when all three observatories record a significant SNR. The O3b source with the best sky localization is GW200311_115853, with a 90% credible area of 35 deg$^2$, which was observed with all three detectors. As the detector network expands, the typical sky-localization precision will improve [25,353].

The volume localization depends upon both the distance and sky localization. The best three-dimensional localizations from O3b are for GW200202_154313 and GW200115_042309, which have 90% credible volumes of 0.0023 and 0.0063 Gpc$^3$, respectively. These correspond to two of the closest sources, with $D_L = 0.41_{-0.16}^{+0.15}$ and $0.29_{-0.10}^{+0.15}$ Gpc, respectively. Using the extended version of the Galaxy List for the Advanced Detector Era (GLADE+) [7,354,355], the 90% credible volume for GW200202_154313 contains approximately 1500 galaxies reported in the K band (approximately 10400 in the bJ band), where we estimate the completeness of the galaxy catalog to be 7%–59% (13%–66%). Similarly, the 90% credible volume for GW200115_042309 contains approximately 5400 galaxies in the K band (approximately 19100 in the bJ band), with estimated completeness of 19%–73% (85%–100%). As the typical distance to sources increases, so will the typical localization volume; however, improvements to detector sensitivity will mean that the localization precision for the best localized sources will improve [25,353,356].

The localization is crucial to multimessenger follow-up efforts. Previously reported candidates have been the target of dedicated follow-up observations. The details of currently reported follow-up observations are reviewed in Appendix A.

### E. Waveform systematics

Our inference of the source properties is dependent on being able to accurately calculate the signal waveform given the source parameters [158,357–363]. The current generation of quasicircular BBH waveforms used here (IMRPhenomXPHM and SEOBNRv4PHM) include higher-order spherical harmonics and model spin precession. Since the waveforms include equivalent physical effects, we expect that any differences that exist are attributable to the particular modeling of the relevant physics. Additionally, IMRPhenomXPHM uses the stationary phase approximation to trade accuracy for faster waveform evaluation in the frequency domain, which produces less reliable descriptions of massive merger-ringdown-dominated signals. To assess the effects of waveform uncertainty on our inferences, and to identify discrepancies that require further study, we compare the results obtained with different waveforms.

The waveforms are calibrated to nonprecessing numerical relativity (NR) waveforms, and good agreement has been found between the two waveform models for non-precessing systems [364]. However, the waveforms are not
calibrated to precessing NR waveforms and use different approximations to describe precession (discussed in Appendix E 2). The lack of accurate information about precession from NR also affects the merger and ringdown portions of the waveform, and the calculation of the quasinormal-mode frequencies. Additional issues regarding an accurate description of precessing systems arise for nearly antialigned spins, where approximations used to model spin effects can break down due to a wide opening angle of the precession cone (for more extreme mass ratios), or instabilities in the spin configuration [365]. Generally, waveforms tend to disagree in parts of the parameter space with higher spins and more extreme mass ratios [137, 273, 364, 366], where the number of NR waveforms available for calibration are limited.

We find that for almost all the signals analyzed here, the differences between results obtained with the IMRPhenomXPHM and SEOBNRv4PHM are subdominant compared to the statistical uncertainty. As for previous observations, differences are typically small, and most noticeable for parameters like the spins [3, 14, 158, 287]. In some cases, there are differences in the multimodality of the posterior probability distribution. Multimodality can be an indication of the complex structure of the waveform and highlight where subtle changes in the modeling may be important. Examples of candidates where there are differences between IMRPhenomXPHM and SEOBNRv4PHM are:

(i) GW191109_010717, which has significant support for negative $\chi_{\text{eff}}$ and misaligned spins, where waveform differences may be expected [364,367]. There are differences in the spins and mass ratio inferred with the two waveforms. Both models show a structured, multimodal joint posterior distribution on $\chi_{\text{eff}}$, q, orbital inclination $\theta_{JN}$ (the angle between the total angular momentum and the line of sight) and $\chi_p$, although the modes are overlapping. SEOBNRv4PHM has a posterior probability distribution with two modes separated mostly in $\theta_{JN}$, one face on and one face off. Both modes show similarly high values of $\chi_p$, and both have $\chi_{\text{eff}} < 0$ with high probability. IMRPhenomXPHM, however, finds a near-edge-on mode ($\theta_{JN} \sim \pi/2$) that prefers more equal component masses, and includes greater support for positive $\chi_{\text{eff}}$. We infer $\chi_{\text{eff}} = -0.31_{-0.32}^{+0.53}$ with IMRPhenomXPHM and $\chi_{\text{eff}} = -0.28_{-0.26}^{+0.26}$ with SEOBNRv4PHM. When a binary is viewed edge on, any precession effects are maximally visible [271, 288, 360, 367, 368].

(ii) GW191219_163120, which has a large mass asymmetry, with the bulk of the posterior probability distribution outside the range of calibration of the waveforms. Despite this, the posteriors obtained with SEOBNRv4PHM and IMRPhenomXPHM show good agreement overall. While the waveforms produce consistent results, there are differences in the

inferred inclination, with IMRPhenomXPHM showing less support for near edge-on orientations; total mass, with IMRPhenomXPHM preferring higher masses, and distance, with IMRPhenomXPHM having less support for larger distances. We infer $q = 0.037_{-0.003}^{+0.004}$ with IMRPhenomXPHM and $q = 0.038_{-0.005}^{+0.006}$ with SEOBNRv4PHM. Modeling of higher-order multipole moments is particularly important for inferring the properties of systems with unequal masses [275, 311, 368–371], and it may impact inference of parameters including the mass ratio, inclination, and distance [3, 178, 362, 372–375].

(iii) GW200129_065458, which has a high SNR ($\rho = 26.8_{-0.2}^{+0.2}$ using IMRPhenomXPHM) and was detected in all three detectors. While both waveforms show approximately the same $\chi_{\text{eff}}$, this candidate shows a high $\chi_p$, as well as stronger support for unequal masses when analyzed with IMRPhenomXPHM, whereas with SEOBNRv4PHM it does not exhibit strong evidence for precession and shows more support for equal masses. We infer $\chi_p = 0.77_{-0.44}^{+0.19}$ and $q = 0.73_{-0.30}^{+0.23}$ with IMRPhenomXPHM, and $\chi_p = 0.36_{-0.25}^{+0.31}$ and $q = 0.901_{-0.169}^{+0.083}$ with SEOBNRv4PHM. Unlike GW191109_010717, the orbital plane is not viewed edge on to the line of sight, so amplitude modulations from precession of the orbital plane are likely to be less significant. However, GW200129_065458 has significant support for inclinations up to $\theta_{JN} \lesssim 1.06$, where precession and higher-order harmonic content may be important [178, 271, 288, 360, 368, 371, 374]. Waveform systematics become more important for higher SNR signals, where statistical uncertainties are smaller [131,361].

(iv) GW200208_222617, which has a multimodal mass posterior and low SNR. The preference for the different modes varies between waveforms. Of the two main modes, the lower-$m_1$-and-$M$ mode is favored by SEOBNRv4PHM, while the higher-$m_1$-and-$M$ mode is favored by IMRPhenomXPHM. Additionally, the IMRPhenomXPHM analysis finds an additional minor mode with $M \sim 175 M_{\odot}$ (visible in Fig. 8 as a protuberance of the 90% contour). The IMRPhenomXPHM analysis also shows a greater preference for higher $\chi_{\text{eff}}$: We infer $\chi_{\text{eff}} = 0.62_{-0.59}^{+0.26}$ with IMRPhenomXPHM, and $\chi_{\text{eff}} = 0.34_{-0.38}^{+0.45}$ with SEOBNRv4PHM.

Future analyses with enhanced waveforms will update our understanding of the source parameters for these candidates.

## VI. WAVEFORM CONSISTENCY TESTS

Waveforms can be reconstructed from the data using two complementary approaches, either using parameter-estimation methods with templates [131,376]
or using minimal modeling [60,377,378]. While the parameter-estimation pipelines directly estimate the match between CBC model waveforms and data, BayesWave (Appendix C) and cWB (Appendix D 5) reconstruct waveforms making only minimal assumptions on the signal shape [60,377,378]. The waveform reconstruction performed by these pipelines uses time-frequency wavelets to identify coherent features in the data, filtering out incoherent noise from the detectors. Although there are similarities between the methods used by cWB [60,109] and BayesWave [377,379], their waveform reconstructions differ in some details. In particular, the point estimate returned by cWB is the constrained maximum-likelihood reconstruction, while for BayesWave we use the median of the time-domain waveform reconstructions from BayesWave’s posterior probability distribution. Examples of both types of reconstruction were reported in GWTC-2 [3].

Starting from minimally modeled waveform reconstructions we can try to detect unexpected behavior by comparing these reconstructions with the CBC waveforms from parameter estimation [3,14,109,380,381]. To test the consistency (or lack thereof) between minimally modeled reconstructions and the CBC waveforms, we perform sets of dedicated injections of CBC waveform samples from the posterior distributions for the source parameters. In these

simulations, the random waveforms are added to background data around the time of the candidates, and the simulated signal is analyzed by the minimally modeled pipelines. We call these off-source injected waveforms, while the reconstructed waveform of the candidate is our on-source result.

Here, as in GWTC-2 [3], we measure the waveform match (or overlap), defined by

$$ \mathcal{O}(h_1, h_2) = \frac{\langle h_1 | h_2 \rangle}{\sqrt{\langle h_1 | h_1 \rangle \langle h_2 | h_2 \rangle}}, \quad (6) $$

where $h_1$ and $h_2$ are two waveforms, $\langle |\cdot| \rangle$ represents the noise-weighted inner product [382], and the match is $-1 \le \mathcal{O}(h_1, h_2) \le 1$. The theoretical definition of match in Eq. (6) does not depend on the amplitude of each signal [3]. However, the addition of noise typically reduces the match value, and the calculated match does depend both on the SNR and, in more detail, on the distribution of signal power in time and frequency. A value of 1 indicates a perfect coincidence between waveforms, while a value close to 0 indicates that the correlation between waveforms is nil. A theoretically possible value of -1 would indicate an improbable perfect anticoincidence. The match is larger for signals corresponding to high-mass systems

<table><caption>TABLE V. List of candidates tested by BayesWave and cWB for consistency with the waveform templates used in the inference of source parameters. We quote the on-source match calculated using the waveform reconstructed for the candidate, and the median and 90% symmetric interval for off-source matches calculated for simulated signals with source parameters consistent with those inferred for the candidate signal. The values reported in the table correspond to those in Fig. 12. Three center dots (···) correspond to candidates not included in an analysis.</caption><thead><tr><th rowspan="2">Candidate</th><th colspan="2">BayesWave</th><th colspan="2">cWB</th></tr><tr><th>On-source match</th><th>Off-source match</th><th>On-source match</th><th>Off-source match</th></tr></thead><tbody><tr><td>GW191109_010717</td><td>0.93</td><td>0.94<sup>+0.04</sup><sub>-0.10</sub></td><td>0.90</td><td>0.90<sup>+0.04</sup><sub>-0.05</sub></td></tr><tr><td>GW191127_050227</td><td>...</td><td>...</td><td>0.86</td><td>0.83<sup>+0.07</sup><sub>-0.10</sub></td></tr><tr><td>GW191129_134029</td><td>0.57</td><td>0.35<sup>+0.26</sup><sub>-0.28</sub></td><td>...</td><td>...</td></tr><tr><td>GW191204_171526</td><td>0.82</td><td>0.68<sup>+0.14</sup><sub>-0.30</sub></td><td>0.91</td><td>0.88<sup>+0.04</sup><sub>-0.07</sub></td></tr><tr><td>GW191215_223052</td><td>0.79</td><td>0.65<sup>+0.17</sup><sub>-0.49</sub></td><td>0.86</td><td>0.80<sup>+0.05</sup><sub>-0.10</sub></td></tr><tr><td>GW191216_213338</td><td>0.73</td><td>0.74<sup>+0.09</sup><sub>-0.42</sub></td><td>...</td><td>...</td></tr><tr><td>GW191222_033537</td><td>0.90</td><td>0.88<sup>+0.06</sup><sub>-0.16</sub></td><td>0.86</td><td>0.81<sup>+0.07</sup><sub>-0.13</sub></td></tr><tr><td>GW191230_180458</td><td>...</td><td>...</td><td>0.85</td><td>0.78<sup>+0.08</sup><sub>-0.11</sub></td></tr><tr><td>GW200128_022011</td><td>...</td><td>...</td><td>0.87</td><td>0.89<sup>+0.04</sup><sub>-0.05</sub></td></tr><tr><td>GW200129_065458</td><td>0.96</td><td>0.96<sup>+0.02</sup><sub>-0.06</sub></td><td>0.80</td><td>0.88<sup>+0.05</sup><sub>-0.09</sub></td></tr><tr><td>GW200208_130117</td><td>0.73</td><td>0.74<sup>+0.14</sup><sub>-0.50</sub></td><td>0.78</td><td>0.79<sup>+0.07</sup><sub>-0.13</sub></td></tr><tr><td>GW200209_085452</td><td>...</td><td>...</td><td>0.82</td><td>0.83<sup>+0.08</sup><sub>-0.09</sub></td></tr><tr><td>GW200216_220804</td><td>...</td><td>...</td><td>0.73</td><td>0.87<sup>+0.05</sup><sub>-0.13</sub></td></tr><tr><td>GW200219_094415</td><td>0.81</td><td>0.74<sup>+0.14</sup><sub>-0.35</sub></td><td>0.81</td><td>0.85<sup>+0.06</sup><sub>-0.08</sub></td></tr><tr><td>GW200224_222234</td><td>0.96</td><td>0.93<sup>+0.03</sup><sub>-0.09</sub></td><td>0.83</td><td>0.84<sup>+0.06</sup><sub>-0.10</sub></td></tr><tr><td>GW200225_060421</td><td>0.85</td><td>0.73<sup>+0.12</sup><sub>-0.38</sub></td><td>0.77</td><td>0.85<sup>+0.07</sup><sub>-0.13</sub></td></tr><tr><td>GW200311_115853</td><td>0.94</td><td>0.90<sup>+0.06</sup><sub>-0.43</sub></td><td>0.93</td><td>0.92<sup>+0.03</sup><sub>-0.04</sub></td></tr></tbody></table>
[380,383–385]. The distribution of match values of the off-source injections defines a null distribution for each candidate; this distribution can be used both to estimate the uncertainty of the observed on-source match value and to obtain a *p*-value from the on-source match. For each candidate, the match is computed off source between injected waveforms and their reconstructions, while on source it is computed between the point estimate of the actual candidate and the maximum-likelihood estimate provided by source-parameter estimation.

The sets of candidates chosen for the BayesWave and cWB consistency tests are different. For the BayesWave analysis we consider candidates that are sufficiently loud and short for BayesWave to produce valid signal reconstructions. The candidates considered by cWB are those detected by the search analysis (reported in Table I), plus five additional candidates that were identified by other search analyses (also reported in Table I). These additional five candidates were reconstructed by the initial stages of the cWB search analysis, but did not pass the cWB postproduction cuts that are used to identify low-FAR candidates (described in Appendix D 5). Both lists are reported in Table V.

The waveform consistency tests are carried out with respect to the results calculated by the Bayesian inference library Bilby [144,146] using the IMRPhenomXPHM waveform [136] (details are presented in Appendix E). Figure 12 shows the on-source match values versus the median off-source match values (together with the 90% intervals). The match values move to lower values for smaller SNR, but the on-source value is still expected to be close to the median of the off-source distribution (blue dashed line in the figure).

if the null hypothesis (that the minimally modeled reconstruction does not deviate significantly from the template-based reconstruction) holds.

Figure 13 shows the *p*-values sorted in increasing order [109,380]. When the null hypothesis holds, the sorted *p*-values are expected to remain close to the median value (orange dashed line); the 90% interval that surrounds the median line shows the size of the fluctuations that we expect to observe. Any significant deviations below the plot diagonal, corresponding to low *p*-values, point to a set of candidates that show potential disagreement with the waveform templates. However, the significance of several simultaneous deviations cannot be directly assessed from the 90% interval, which is calculated for single values [386]. Since the *p*-values are sorted in increasing order, the sorting induces a correlation between successive values, and this means that there may be a whole subset of points outside the interval. All of the 15 cWB *p*-values are within the 90% interval. This is not the case for BayesWave, where it is important to consider the finite-size effect due to the limited number of off-source samples in the match distribution. The posterior probability distribution for the *p*-value estimate due to the finite-size effect is Beta(*n* + 1, *N* − *n* + 1), where *N* is the total number of samples, and *n* is the number of samples with a match value less than the on-source match [6]. In addition to the 90% interval associated with the statistical distribution of *p*-values for the null hypothesis, the *p*-value plots in Fig. 13 also display the 90% interval from the finite-size effect: We see that after including this effect, there are four out of 12 incompatible *p*-values (where the 90% intervals

<figure><img src="image_15.png" /></figure>

FIG. 12. Off-source versus on-source match values for the candidates in O3b. The left and right panels show the results of the BayesWave and cWB analyses, respectively. The on-source match is estimated comparing the inferred maximum-likelihood CBC waveform with point estimates from the minimally modeled waveform reconstructions. The off-source match is the median value of the match distribution estimated from off-source injection of sample waveforms from the template-based posterior distribution. The error bars in both panels are given by the symmetric (equal-tailed) 90% confidence interval, and they mark the distance from the null hypothesis (blue dashed line). The different sizes of the error bars in the two panels is due to the different numbers of off-source injections in the BayesWave and cWB analyses.
<figure><img src="image_16.png" /><figcaption>FIG. 13. Distribution of *p*-values for the O3b candidates reconstructed by the minimally modeled pipelines. The left and right panels report the *BayesWave* and *cWB* results, respectively. The *p*-values are sorted in increasing order and graphed against the order number (blue dashed line). Each *p*-value is estimated from the observed on-source match value and the related off-source distribution of the match values from off-source injections. The shadowed orange band is the symmetric 90% interval about the median, represented by the orange solid line. The blue band represents the symmetric 90% interval associated with the finite number of off-source injections.</figcaption></figure>

do not overlap). Finding four incompatible *p*-values is not an unlikely event, it has approximately 4.1% probability of being due to chance. We conclude that both the match-match and the *p*-value plots indicate that there is no significant inconsistency between the minimally modeled waveform reconstruction and the results of the parameter-estimation analysis. Further checks of the consistency of the signals, focused on the predictions from general relativity, are given in a companion paper [6].

## VII. CONCLUSION

We present the latest LVK catalog of GWs, which contains a total of 90 CBC candidate signals with an estimated probability of astrophysical origin $p_{astro} > 0.5$. GWTC-3 builds upon past catalogs of GW candidates from O1 [13], O2 [14], and O3a [3,4], adding an additional 35 candidates from O3b with $p_{astro} > 0.5$. These include the NSBH candidates GW191219_163120 and GW200115_042309, as well as the candidate GW200210_092254 that could potentially be either from a NSBH or a BBH. We additionally provide a list of candidates with $p_{astro} < 0.5$ meeting a FAR threshold of <2.0 day⁻¹. This includes GW200105_162426, which is estimated to have $p_{astro} = 0.36$ but is a clear outlier from our background noise distribution, and is inferred to have a NSBH source [8]. While we expect approximately four to six of the candidates with $p_{astro} > 0.5$ to be false alarms, we also expect approximately seven candidates with $p_{astro} < 0.5$ to be astrophysical GW signals. GW observations of CBCs provide new insight into diverse areas of physics ranging from binary stellar evolution to gravitation. Further analysis

and interpretation of the GWTC-3 candidates is conducted in the companion papers [5–7]. As the population of GW observations grows, it will be possible to make increasingly detailed measurements of compact-object physics.

The growing catalog of GW sources has revealed a diversity of potential CBC sources. Among the candidates are a few with posterior support for high spins ($\chi_i \gtrsim 0.8$) and large mass asymmetries ($q \lesssim 0.1$). Creating waveform models in these regimes is challenging, as the need to maintain accuracy necessitates more complete prescriptions of the underlying physics, including effects such as spin-induced precession [387,388] plus higher-order multipole moments [178,357,362,374]. This task is further complicated by the lack of extensive NR waveform catalogs covering these regions of parameter space [389–392]. As sensitivity improves, waveform uncertainty may be a significant source of systematic uncertainty [360,361]. Therefore, to ensure reliable interpretation of GW observations in the future, it is imperative to develop improved waveform models that cover a wider range of source properties, and include potentially important additional physics such as orbital eccentricity [393–398].

Data products associated with GWTC-3 results are available through GWOSC [33] in addition to the full O3b detector strain data [399,400]. Release of previous observing runs' strain data [400,401] has enabled multiple independent analyses of LIGO and Virgo data, including identification of additional detection candidates [15–20,104,105,210,402–404]. Therefore, we anticipate that further discoveries may come from O3b data.

O3 saw the Advanced LIGO and Advanced Virgo detectors reach their greatest sensitivity to date, enabling
an unprecedented rate of discovery. Coupled to the longer duration of O3 compared to previous observing runs, this sensitivity has enabled the number of GW detections from O3 to significantly exceed that from O1 and O2. The Advanced LIGO and Advanced Virgo detectors are currently offline undergoing commissioning to further enhance their performance for O4. O4 will also see the joint operation of the KAGRA detector [405]. KAGRA successfully completed a joint observing run with GEO 600 following the end of O3 for Advanced LIGO and Advanced Virgo [406], and O4 will be the first opportunity for observations from the LIGO-Virgo-KAGRA detector network. The enhanced O4 global detector network will further increase the prospects for GW and multimessenger discoveries [25].

While the 90 probable GW candidates of GWTC-3 all correspond to CBC sources, we anticipate that there are other GW signals waiting to be found [407]. These could include new types of transient signal, such as from supernovae [408], cosmic strings [30], or previously unidentified sources [31,32]. Additionally, we may find long-lived signals such as continuous waves from rotating NSs [409–414] or stochastic backgrounds [415,416]. As detector sensitivity increases and we observe for longer, we expect more of the GW universe to reveal itself.

## ACKNOWLEDGMENTS

Calibration of the LIGO strain data was performed with GstLAL-based calibration software pipeline [45]. Calibration of the Virgo strain data is performed with c-based software [53]. Data-quality products and event-validation results were computed using the DMT [417], DQR [76], DQSEGDB [418], GWDETCHAR [419], HVETO [420], iDQ [421], Omicron [65] and PYTHONVIRGOTOOLS [422] software packages and contributing software tools. Analyses in this catalog relied upon the LALSuite software library [423]. The detection of the signals and subsequent significance evaluations in this catalog were performed with the GstLAL-based inspiral software pipeline [78–81], with the MBTA pipeline [82,83], and with the PyCBC [86–88] and the cWB [60,89,90] packages. Estimates of the noise spectra and glitch models were obtained using BayesWave [377,379,383]. Noise subtraction for one candidate was also performed with gwsubtract [44]. Source-parameter estimation was performed with the Bilby and Parallel Bilby libraries [144–146] using the Dynasty nested sampling package [424], and the RIFT library [147–149], with the LALInference [376] libraries used for initial analyses. PESUMMARY was used to postprocess and collate parameter-estimation results [425]. The various stages of the parameter-estimation analysis were managed with the Asimov library [426]. Plots were prepared with MATPLOTLIB [427], SEABORN [428] and GWPy [429]. NumPy [430] and SciPy [431] were used in the preparation of the manuscript. This material is based upon work supported by NSF's

LIGO Laboratory which is a major facility fully funded by the National Science Foundation. The authors also gratefully acknowledge the support of the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society, and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO 600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS), and the Netherlands Organization for Scientific Research, for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, the Department of Science and Technology, India, the Science & Engineering Research Board, India, the Ministry of Human Resource Development, India, the Spanish Agencia Estatal de Investigación, the Vicepresidència i Conselleria d'Innovació, Recerca i Turisme, and the Conselleria d'Educació i Universitat del Govern de les Illes Balears, the Conselleria d'Innovació, Universitats, Ciència i Societat Digital de la Generalitat Valenciana, and the CERCA Programme Generalitat de Catalunya, Spain, the National Science Centre of Poland and the Foundation for Polish Science, the Swiss National Science Foundation, the Russian Foundation for Basic Research, the Russian Science Foundation, the European Commission, the European Regional Development Funds, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund, the French Lyon Institute of Origins, the Belgian Fonds de la Recherche Scientifique, Actions de Recherche Concertées and Fonds Wetenschappelijk Onderzoek—Vlaanderen, Belgium, the Paris Île-de-France Region, the National Research, Development and Innovation Office Hungary, the National Research Foundation of Korea, the Natural Science and Engineering Research Council Canada, Canadian Foundation for Innovation, the Brazilian Ministry of Science, Technology, and Innovations, the International Center for Theoretical Physics South American Institute for Fundamental Research, the Research Grants Council of Hong Kong, the National Natural Science Foundation of China, the Leverhulme Trust, the Research Corporation, the Ministry of Science and Technology, Taiwan, the United States Department of Energy, and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, INFN, and CNRS for provision of computational resources. Computing was performed on the OzSTAR Australian national facility at Swinburne University of Technology, which receives funding in part from the Astronomy National Collaborative Research Infrastructure Strategy allocation
provided by the Australian Government. We thankfully
acknowledge the computer resources at MareNostrum
and the technical support provided by Barcelona
Supercomputing Center (Grant No. RES-AECT-2021-2-
0021). This work was supported by MEXT, JSPS Leading-
edge Research Infrastructure Program, JSPS Grant-in-Aid
for Specially Promoted Research, Grant No. 26000005,
JSPS Grant-in-Aid for Scientific Research on Innovative
Areas 2905: Grants No, JP17H06358, No. JP17H06361,
and No. JP17H06364, JSPS Core-to-Core Program A.
Advanced Research Networks, JSPS Grant-in-Aid for
Scientific Research (S) Grant No. 17H06133, the joint
research program of the Institute for Cosmic Ray Research,
University of Tokyo, National Research Foundation and
Computing Infrastructure Project of KISTI-GSDC in Korea,
Academia Sinica, AS Grid Center and the Ministry of
Science and Technology in Taiwan under grants including
Grant No. AS-CDA-105-M06, Advanced Technology
Center of NAOJ, and Mechanical Engineering Center of
KEK. We thank the anonymous journal referees for helpful
comments.

APPENDIX A: LOW-LATENCY ALERT SYSTEM
AND MULTIMESSENGER FOLLOW-UP

Public alerts are issued for GW candidates identified by
low-latency searches of the data. These candidates are
cataloged in the Gravitational Candidate Event Database
(GraceDB). Each entry into GraceDB is known as an event,
and a collection of these within a specific time window is
referred to as a superevent. The time window for CBC
events is variable based on the spread of events, with a
typical value of 1-s symmetric around the merger time. The
duration of the time window for cWB is variable and is
reported by the search pipeline for each event. One
candidate event belonging to the superevent is identified
as the preferred event, and its attributes (time, localization,
significance, classification, and properties) [115,129,432]
are inherited by the superevent. The HasRemnant property
indicator is related to the probability of having an electro-
magnetic counterpart [432], and the p_astro classifier assigns
a source-category-based astrophysical probability under
the assumption that astrophysical and terrestrial triggers
occur as independent Poisson processes [112,115]. The
name of a superevent is its uniquely assigned identi-
fication in GraceDB consisting of three parts: the prefix
S (for superevent), the six-digit UTC date of the event
(YYMMDD), and a lowercase alphabetic suffix.

During O3, CBC superevents that passed a FAR threshold
of one per two months and generic transient (Burst) super-
events that passed a FAR threshold of one per year were
distributed as public alerts. The individual FAR thresholds of
each pipeline are corrected by a trials factor to account for the
data being analyzed by multiple pipelines. Generally, multi-
ple pipelines identify the candidate GW events distributed as
public alerts.

When a preferred event candidate passes the public-alert
threshold, a preliminary alert is queued, while new event
candidates are still accepted to be added to the superevent.
After the preliminary alert reception by the GCN broker,
the preferred event is revised and a second preliminary
Notice is issued, even if the preferred event candidate
remains unchanged. The alerts are processed by the
GWCelery distributed task queue software [11,433], which
organizes basic data-quality checks, groups events from
online searches, and initiates localization and inference of
source properties.

As in O2 [434], human vetting of the superevents is a
critical part of the online program, and is completed once
the superevent passed the public-alert threshold. The rapid-
response team consists of commissioning, computing, and
calibration experts from each of the detector sites, search-
pipeline experts, detector-characterization experts, and
follow-up advocates in charge of the delivery of the initial
GCN Notice and Circular. A data-quality report is also
initiated by GWCelery, and consists of a semiautomated
detector-characterization and data-quality investigation. It
provides a variety of metrics based on auxiliary instru-
mental and environmental sensors to help the rapid-
response team make a decision whether to confirm or
retract a candidate. The preliminary alerts were typically
issued within a few minutes of data collection, for which
latency due to data transfer between sites and search
investigation are largely dominated by the GWCelery task.
The human vetting and delivery of initial alerts had a
median duration of approximately 30 min.

There were 40 public alerts sent out via GCN during O3a
and 39 during O3b. Of these, 33 from O3a and 23 from O3b
were not retracted; the remaining were retracted on time-
scales from minutes to days. The majority of the retracted
public alerts in O3b correspond to candidates with SNR
ρ > 5 in only one detector. The online search pipelines
collect background in real time, leaving them susceptible to
new noise sources, and single-detector candidates are
especially impacted by uncertainties in the background
noise distribution since they cannot rely on coincidence to
establish significance. Among the remaining O3b alerts,
22 involve CBC candidates, and one (S200114f) is a Burst
candidate, as discussed in Sec. IV D 1. The unretracted
O3a alerts are publicly distributed in 7.3+56/2 min, and the
O3b alerts in 5.8+377/3 min (median and 90% symmetric
interval). One O3b candidate, S200303ba, is retracted
but never has a preliminary Notice sent out due to pro-
blems connecting to the GCN broker. The GW candidate
alerts generated 1513 Circulars during O3 (44% of 3463
GCN Circulars in the same period), with 967 and 546
Circulars (64% and 36%) sent during O3a and O3b,
respectively.

Follow-up observations were made by teams across the
astronomical community, culminating in GCN Circulars
and papers. The searches for multimessenger counterparts
<table><caption>TABLE VI. Public alerts and follow-up investigations of O3a GW candidates. The columns show the superevent identification (SID), the GW candidate name if in offline results [3,4], the GCN Circular, and references for follow-up publications. Candidates retracted following rapid event-validation checks are marked in italics. Candidates without superevent identifications were found only in the offline searches.</caption><thead><tr><th>SID</th><th>Event</th><th>GCN</th><th>Follow-up publications</th></tr></thead><tbody><tr><td>S190408an</td><td>GW190408_181802</td><td>[436]</td><td>[437-457]</td></tr><tr><td>S190412m</td><td>GW190412</td><td>[458]</td><td>[437-451,453,455-457,459-461]</td></tr><tr><td></td><td>GW190413_052954</td><td></td><td>[437-439,441,446,448,453,457,459]</td></tr><tr><td></td><td>GW190413_134308</td><td></td><td>[437-439,441,446,448,453,457,459]</td></tr><tr><td>S190421ar</td><td>GW190421_213856</td><td>[462]</td><td>[437-449,451,453,455-457,459]</td></tr><tr><td></td><td>GW190424_180648</td><td></td><td>[437,441,446,448,453,457,459]</td></tr><tr><td>S190425z</td><td>GW190425</td><td>[463]</td><td>[437-449,451-453,455-457,459-461,464-472]</td></tr><tr><td>S190426c</td><td>GW190426_152155</td><td>[473]</td><td>[437,439-449,451-453,455-457,459-461,465-470,474-477]</td></tr><tr><td>S190503bf</td><td>GW190503_185404</td><td>[478]</td><td>[437-444,446,448-451,453,455,457,459]</td></tr><tr><td>S190510g</td><td></td><td>[479]</td><td>[440,443,444,447,449,451,455,456,460,461,466,467,474,480,481]</td></tr><tr><td>S190512at</td><td>GW190512_180714</td><td>[482]</td><td>[437-441,443,444,446-449,451,453,455,457,459,483-485]</td></tr><tr><td>S190513bm</td><td>GW190513_205428</td><td>[486]</td><td>[437-441,443-449,451,453,455,457,459]</td></tr><tr><td></td><td>GW190514_065416</td><td></td><td>[437-439,441,446,448,453,457,459]</td></tr><tr><td>S190517h</td><td>GW190517_055101</td><td>[487]</td><td>[437-444,446-449,451,453,455,457,459]</td></tr><tr><td>S190518bb</td><td></td><td>[488]</td><td></td></tr><tr><td>S190519bj</td><td>GW190519_153544</td><td>[489]</td><td>[437-439,441-443,446,448,451,453,457,459]</td></tr><tr><td>S190521g</td><td>GW190521</td><td>[490]</td><td>[437-449,451,453-455,457,459,491,492]</td></tr><tr><td>S190521r</td><td>GW190521_074359</td><td>[493]</td><td>[437-449,451,453,455-457,459]</td></tr><tr><td>S190524q</td><td></td><td>[494]</td><td></td></tr><tr><td></td><td>GW190527_092055</td><td></td><td>[437-439,441,446,448,453,457,459]</td></tr><tr><td>S190602aq</td><td>GW190602_175927</td><td>[495]</td><td>[437-444,446,448,449,451,453,455,457,459]</td></tr><tr><td></td><td>GW190620_030421</td><td></td><td>[437-439,441,446,448,453,457,459]</td></tr><tr><td>S190630ag</td><td>GW190630_185205</td><td>[496]</td><td>[437-439,441-443,446,448,451,453,457,459]</td></tr><tr><td>S190701ah</td><td>GW190701_203306</td><td>[497]</td><td>[437-440,442-444,446,448,449,451,453,455,457,459]</td></tr><tr><td>S190706ai</td><td>GW190706_222641</td><td>[498]</td><td>[437-440,442-449,451,453,455,457,459]</td></tr><tr><td>S190707q</td><td>GW190707_093326</td><td>[499]</td><td>[437-440,442-444,446-449,451,453,455,457,459]</td></tr><tr><td></td><td>GW190708_232457</td><td></td><td>[437-439,446,448,453,457,459]</td></tr><tr><td>S190718y</td><td></td><td>[500]</td><td>[440,443,444,447,449,451,455,460,461]</td></tr><tr><td></td><td>GW190719_215514</td><td></td><td>[437-439,446,448,453,457,459]</td></tr><tr><td>S190720a</td><td>GW190720_000836</td><td>[501]</td><td>[437-440,443,444,446-449,451,453,455-457,459]</td></tr><tr><td>S190727h</td><td>GW190727_060333</td><td>[502]</td><td>[437-440,443,444,446-449,451,453,455,457,459]</td></tr><tr><td>S190728q</td><td>GW190728_064510</td><td>[503]</td><td>[437-440,443,444,446-449,451,453,455-457,460,483,484,504]</td></tr><tr><td></td><td>GW190731_140936</td><td></td><td>[437-439,446,448,453,457,459]</td></tr><tr><td></td><td>GW190803_022701</td><td></td><td>[437-439,446,448,453,457,459]</td></tr><tr><td>S190808ae</td><td></td><td>[505]</td><td>[460]</td></tr><tr><td>S190814bv</td><td>GW190814</td><td>[506]</td><td>[438-440,443-448,451,453,455,456,459-461,470,507-518]</td></tr><tr><td>S190816i</td><td></td><td>[519]</td><td></td></tr><tr><td>S190822c</td><td></td><td>[520]</td><td>[460,461]</td></tr><tr><td>S190828j</td><td>GW190828_063405</td><td>[521]</td><td>[437-440,443-448,451,453,455,457,459]</td></tr><tr><td>S190828l</td><td>GW190828_065509</td><td>[522]</td><td>[437-440,443,444,446-448,451,453,455,457,459]</td></tr><tr><td>S190829u</td><td></td><td>[523]</td><td></td></tr><tr><td>S190901ap</td><td></td><td>[524]</td><td>[440,443,444,447,451,454-456,466,468,470,510]</td></tr></tbody></table>

(Table continued)
<table><caption>TABLE VI. (Continued)</caption><thead><tr><th>SID</th><th>Event</th><th>GCN</th><th>Follow-up publications</th></tr></thead><tbody><tr><td>S190910d</td><td>GW190909_114149</td><td>[525]</td><td>[437,446,448,453,459]</td></tr><tr><td>S190910h</td><td>GW190910_112807</td><td>[526]</td><td>[440,443,444,447,451,455,457,466,510]</td></tr><tr><td>S190915ak</td><td>GW190915_235702</td><td>[527]</td><td>[437,439,446,453]</td></tr><tr><td>S190923y</td><td></td><td>[528]</td><td>[440,443,444,447,451,454–456,468,470]</td></tr><tr><td>S190924h</td><td>GW190924_021846</td><td>[529]</td><td>[437–440,443,444,446–448,451,453,455,459]</td></tr><tr><td>S190928c</td><td>GW190929_012149</td><td>[530]</td><td>[437–439,446,457,459]</td></tr><tr><td>S190930s</td><td>GW190930_133541</td><td>[531]</td><td>[437–440,443–448,451,453,455,456,459]</td></tr><tr><td>S190930t</td><td></td><td>[532]</td><td>[440,443,444,447,451,453–456,460,470]</td></tr></tbody></table>

employed the same variety of observing strategies used for previous observing runs [434], including archival analysis, prompt searches with all-sky instruments, wide-field tiled searches, targeted searches of potential host galaxies, and deep follow-up of individual sources. The follow-up effort mobilized a total of about 100 ground- and space-based instruments such as neutrino observatories, very-high-energy gamma-ray observatories, space-based gamma-ray and x-ray instruments, visible and infrared telescopes, and

radio telescopes. The latency for follow-up observations, analyses, public reporting of results, and the process efficiency varied across the collaborations and the multi-messenger probe involved. Additionally, the public alerts enabled amateur astronomers to join professional astronomers in the search for electromagnetic counterparts [435]. Summaries of the O3a and O3b candidates with public alerts and follow-up investigations are reported in Tables VI and VII, respectively.

<table><caption>TABLE VII. Public alerts and follow-up investigations of O3b GW candidates. The columns show the superevent identification (SID), the GW candidate name if in the offline results (including GW200105_162426), the GCN Circular, and references for follow-up publications. Candidates retracted following rapid event-validation checks are marked in italics. Candidates without superevent identifications were found only in the offline searches.</caption><thead><tr><th>SID</th><th>Event</th><th>GCN</th><th>Follow-up publications</th></tr></thead><tbody><tr><td>S191105e</td><td>GW191105_143521</td><td>[533]</td><td>[435,437–440,443,445,448,451,453,455,456,459]</td></tr><tr><td>S191109d</td><td>GW191109_010717</td><td>[534]</td><td>[435,437–440,443,445,448,451,453,455,459]</td></tr><tr><td>S191110af</td><td></td><td>[535]</td><td>[460,461]</td></tr><tr><td>S191110x</td><td></td><td>[536]</td><td></td></tr><tr><td>S191117j</td><td></td><td>[537]</td><td></td></tr><tr><td>S191120aj</td><td></td><td>[538]</td><td></td></tr><tr><td>S191120at</td><td></td><td>[539]</td><td></td></tr><tr><td>S191124be</td><td></td><td>[540]</td><td></td></tr><tr><td>S191129u</td><td>GW191129_134029</td><td>[541]</td><td>[435,437–440,443,448,451,453,455,459]</td></tr><tr><td>S191204r</td><td>GW191204_171526</td><td>[542]</td><td>[435,437–440,443,445,448,451,453,455,459]</td></tr><tr><td>S191205ah</td><td></td><td>[543]</td><td>[435,440,443,445,451,454,456,468,470]</td></tr><tr><td>S191212q</td><td></td><td>[544]</td><td>[437]</td></tr><tr><td>S191213g</td><td></td><td>[545]</td><td>[435,437,440,443,451,454,455,460,461,468,470,476]</td></tr><tr><td>S191213ai</td><td></td><td>[546]</td><td></td></tr><tr><td>S191215w</td><td>GW191215_223052</td><td>[547]</td><td>[435,438–440,443,445,448,451,453,455,459]</td></tr><tr><td>S191216ap</td><td>GW191216_213338</td><td>[548]</td><td>[435,437–440,443,445,448,451,453,455,456,459–461,504,549]</td></tr><tr><td>S191220af</td><td></td><td>[550]</td><td>[466]</td></tr><tr><td>S191222n</td><td>GW191222_033537</td><td>[551]</td><td>[435,437,438,440,443,448,451,453,455,459]</td></tr></tbody></table>

(Table continued)