<table><caption>TABLE VII. (Continued)</caption><thead><tr><th>SID</th><th>Event</th><th>GCN</th><th>Follow-up publications</th></tr></thead><tbody><tr><td>S191225aq</td><td></td><td>[552]</td><td></td></tr><tr><td>S200105ae</td><td>GW200105_162426</td><td>[553]</td><td>[435,437-440,443,448,451,454,455,457,459,470,484,554]</td></tr><tr><td>S200106au</td><td></td><td>[555]</td><td></td></tr><tr><td>S200106av</td><td></td><td>[555]</td><td></td></tr><tr><td>S200108v</td><td></td><td>[556]</td><td></td></tr><tr><td>S200112r</td><td>GW200112_155838</td><td>[557]</td><td>[435,437-440,443,448,451,453,455,459]</td></tr><tr><td>S200114f</td><td></td><td>[558]</td><td>[440,443,445,451,454-456,460,461]</td></tr><tr><td>S200115j</td><td>GW200115_042309</td><td>[559]</td><td>[435,437-440,443,445,448,451,453-455,457,459-461,468,470,484,554,560]</td></tr><tr><td>S200116ah</td><td></td><td>[561]</td><td></td></tr><tr><td>S200128d</td><td>GW200128_022011</td><td>[562]</td><td>[435,437-440,443,448,451,453,455,459]</td></tr><tr><td>S200129m</td><td>GW200129_065458</td><td>[563]</td><td>[435,437-440,443,448,451,453,455,459]</td></tr><tr><td>S200208q</td><td>GW200208_130117</td><td>[564]</td><td>[435,437-440,443,448,451,453,455,459]</td></tr><tr><td>S200213t</td><td></td><td>[565]</td><td>[435,437,440,443,445,451,455,456,460,461,468,470,476,504]</td></tr><tr><td>S200219ac</td><td>GW200219_094415</td><td>[566]</td><td>[435,437-440,443,445,448,451,453,455,456,459,567]</td></tr><tr><td>S200224ca</td><td>GW200224_222234</td><td>[568]</td><td>[435,437-440,443,445,448,451,453-456,459-461,483,569-571]</td></tr><tr><td>S200225q</td><td>GW200225_060421</td><td>[572]</td><td>[435,437-440,443,445,448,451,453,455,456,459-461]</td></tr><tr><td>S200302c</td><td>GW200302_015811</td><td>[573]</td><td>[435,437-440,443,448,451,453,455,459,574]</td></tr><tr><td>S200303ba</td><td></td><td>[575]</td><td></td></tr><tr><td>S200308e</td><td></td><td>[576]</td><td>[439]</td></tr><tr><td>S200311bg</td><td>GW200311_115853</td><td>[577]</td><td>[435,437-440,443,448,451,453,455,459]</td></tr><tr><td>S200316bj</td><td>GW200316_215756</td><td>[578]</td><td>[435,437-440,443,445,448,451,453-455]</td></tr></tbody></table>

The two alerts with the largest number of GCN Circulars distributed during O3a are GW190814 (S190814bv), whose source is a potential NSBH or low-mass BBH coalescence [241,507-509,511,514,515,517,518] and the BNS GW190425 (S190425z) [159,469,510]. A potential association between GW190425 and the fast radio burst FRB 20190425A [579] occurring 2.5 h after the merger, has been suggested [580], but a late-time optical and radio search 2.5-yr postburst is negative [471]. S191213g, the first O3b BNS candidate, has the largest number of GCN Circulars during O3b, a total of 53 [545] (but it is only in fifth position considering the whole of O3). As discussed in Sec. IV D, S191213g was not identified as a significant candidate in the offline search results. The O3 candidates are predominantly BBHs, where counterparts are not typically expected unless the system has surrounding gas [581-586].

The neutrino follow-up involved searches of events with energies ranging from approximately 1 MeV to approximately 1 PeV. No confirmed neutrino counterpart has been found for any GW candidate [437-442,449,457,459,587].

The gamma- and x-ray observations involved energies extending up to approximately 1 TeV. The majority of high-energy searches report no candidates [443,461,472,483,484,492,504,518,569,588].

The optical and near-infrared teams focused mainly on the non-BBH systems or well-localized and nearby candidates.

Often, multiple optical telescopes worked in synergy for the identification and characterization of counterparts [435,447,456,470,574]. Several surveys performed systematic prompt follow-up searches for counterparts for a large number of candidates [445,448,450-454,466,474]. No confirmed prompt optical or infrared counterpart has been detected for O3 candidates.

The follow-up in the radio domain was mostly focused on the characterization of specific candidate counterparts, either neutrino, x-ray, or optical candidates [464,512,549]. No confirmed radio counterparts have been reported, with the possible exception of the fast radio burst associated with GW190425 [580].

Nondetection of electromagnetic counterparts in follow-up searches for candidates where at least one component could be a NS can potentially set constraints on the ejected matter; however, current observations cannot provide strong constraints [467,589]. It has been suggested that due to their faintness and fast evolution, searches by optical surveys for kilonovas within a distance up to 200 Mpc require early observations down to magnitude 21 [590]. Future counterpart detections as soon as the next observing run are likely to place strong, multimessenger constraints on the equation of state of NSs, and the Hubble constant [591-595].

Additional specific counterpart searches have been performed after alerts, based on properties of the GW
candidates and using all-sky, multiwavelength data. As an illustration, GW190521, a signal from a high-mass BBH [4,184], generated interest due to the possible association with an observed flare of the active galactic nucleus AGN J124942.3+344929 [491]. This association, while still uncertain [19,596–598], highlights the potential discoveries that could be made by searching for counterparts to BBH coalescences, as well as the scope for detections of counterparts in archival searches.

## APPENDIX B: OBSERVATORY EVOLUTION

From the start of the advanced-detector era in O1 through O3b, the network of GW observatories has undergone a variety of commissioning activities to improve performance [25]. The configurations of the detectors were different in O1 [13], O2 [14,304], and O3 [38,64]. O2 marked the first operation of the three-detector LIGO-Virgo network, and Fig. 14 shows the O2 and O3b sensitivities for all interferometers to illustrate the evolution in performance. Key parameters describing the LIGO detectors and Virgo are reported in Table VIII, specifically: input laser power (estimated at the power recycling mirror after exiting the input mode cleaner); power recycling gain (the ratio of stored power in the power recycling cavity to the input laser power, which depends on the reflectivities of the test masses and power recycling mirror, as well as the losses in the arms and the power recycling cavity [599]); the presence of signal recycling; adoption of squeezed light, and suspension type. The main upgrade from run to run for all interferometers was the increase in the input laser power, which is instrumental in reducing shot noise. Signal recycling mirrors [600] are presently installed only in the LIGO interferometers [1]. While in Hanford and

Livingston, monolithic test-mass suspensions have been operating since O1, they were installed in Virgo only for O3, replacing the wire suspensions used during O2. Squeezing was implemented during O3 at all sites [601,602]. More details on the hardware and software changes that the LIGO Hanford, LIGO Livingston and Virgo observatories underwent from O3a to O3b are given below.

### 1. LIGO Hanford and Livingston Observatories

The sensitivities of the Hanford and Livingston interferometers during O3b were similar to during O3a [3,38]. The upgrades between O3a and O3b aimed to address not only noise couplings that affect the range, but also reduce light scattering that degrades data quality, and improve resilience against environmental conditions that affect duty cycle.

High optical power in the interferometer reduces the shot noise. The current limit on the maximum circulating power of both LIGO interferometers [599] is from point defects in the test-mass mirror optical coatings which absorb and scatter light. Point absorbers appear in both the LIGO Hanford and Livingston interferometers, and may be identified using Hartmann wave-front sensors, which can measure distortions created by point defects [603,604]. Prior to O3b, both end test masses at LIGO Livingston were inspected with a microscope to investigate potential defects. After this investigation, new point absorbers appeared on both of these end test masses [605,606] for reasons not yet known [599]. These new absorbers resulted in increased optical losses, a reduction in circulating power, and a consequent degradation of the Livingston interferometer's BNS inspiral range due to increased shot noise of approximately 5 Mpc.

Adjustments to the squeezing subsystem produced the largest range improvements during O3b shown in the left panel of Fig. 3. An in-vacuum squeezer was installed for the O3 run at both LIGO sites to improve detector sensitivity above approximately 55 Hz [601], below which radiation-pressure noise is larger with squeezing than the shot-noise level without squeezing. The squeezer works by optically pumping a nonlinear crystal to create correlated photons. The correlations modify the distribution of uncertainty in the quantum state that enters the interferometer [39,40]. The squeezer crystal has been found to degrade on timescales between a week and a month, reducing the pump light power and diminishing the squeezing below its optimal level. At LIGO Livingston, increased squeezing from moving the spot position on the crystal recovered approximately 3 Mpc in BNS inspiral range between O3a and O3b. At LIGO Hanford, a damaged fiber delivering pump light to the crystal was replaced between O3a and O3b, allowing a threefold increase in pump power and more squeezing. Adjustments done between O3a and O3b, in conjunction with moving the

<figure><img src="image_17.png" /><figcaption>FIG. 14. Representative noise amplitude spectral densities for LIGO Livingston, LIGO Hanford, Virgo during O2 and O3b.</figcaption></figure>
<table><caption>TABLE VIII. Summary of selected optical and physical parameters of the LIGO Hanford (H), LIGO Livingston (L), and Virgo (V) interferometers in the advanced-detector era. The input laser power is an estimate for the maximum laser power level typically achieved during the observing period, and is the power that would be measured at the power recycling mirror (after the input mode cleaner). The suspension type is abbreviated as Silica for monolithic fused-silica fibers and Steel for steel wires.</caption><thead><tr><th rowspan="2">Parameter</th><th colspan="2">O1</th><th colspan="3">O2</th><th colspan="3">O3a</th><th colspan="3">O3b</th></tr><tr><th>H</th><th>L</th><th>H</th><th>L</th><th>V</th><th>H</th><th>L</th><th>V</th><th>H</th><th>L</th><th>V</th></tr></thead><tbody><tr><td>Input laser power</td><td>21 W</td><td>22 W</td><td>26 W</td><td>25 W</td><td>10 W</td><td>34 W</td><td>44 W</td><td>18 W</td><td>34 W</td><td>40 W</td><td>26 W</td></tr><tr><td>Power recycling gain</td><td>38</td><td>38</td><td>40</td><td>36</td><td>38</td><td>44</td><td>47</td><td>36</td><td>44</td><td>42</td><td>34</td></tr><tr><td>Signal recycling</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✗</td><td>✓</td><td>✓</td><td>✗</td><td>✓</td><td>✓</td><td>✗</td></tr><tr><td>Squeezing</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Suspension type</td><td>Silica</td><td>Silica</td><td>Silica</td><td>Silica</td><td>Steel</td><td>Silica</td><td>Silica</td><td>Silica</td><td>Silica</td><td>Silica</td><td>Silica</td></tr></tbody></table>

crystal position and retuning the squeezer on 2 January 2020 during O3b (shown in Fig. 3), produced an improvement of approximately 7 Mpc in Hanford’s BNS inspiral range.

O3b includes upgrades to the LIGO detectors to reduce scattered-light noise. Scattered-light noise occurs when a fraction of light gets scattered from its intended path, hits another moving surface, and a part of this light gets reflected back, rejoining the main interferometer beam with a noisy, varying phase [67,68]. This noise can be up-converted to higher harmonics of the surface motion frequencies, causing glitches. At LIGO Livingston, several locations at both end stations are outfitted with improved light baffles to prevent scattered light reflected off the vacuum envelope from recoupling with the main beam. A particularly important contribution was new baffles installed between O3a and O3b surrounding a suspended platform that relay a beam transmitted by one end test mass. At LIGO Hanford, a window in the output optic chain was replaced between O3a and O3b with one that has a larger incidence angle to ensure the back reflection from the window could not be a source of scattered light. Scattered-light noise is found to be correlated to microseismic activity, which is ground motion in the frequency band 0.1–0.5 Hz driven primarily by oceanic waves. During periods of high microseismic activity, both Hanford and Livingston interferometers suffer from large relative motion between the end test mass and the reaction mass that is immediately behind the test mass. This motion is found to produce a scattered-light noise path contributing to transient noise in the interferometer output [69]. This noise is mitigated by implementing reaction-chain tracking, a control loop that makes the reaction mass follow the end test mass, reducing the relative motion. Reaction-chain tracking was implemented on 7 January 2020 and 14 January 2020 at Livingston and Hanford, respectively. These efforts to reduce scattered-light noise had a significant effect on data quality by reducing transient noise as discussed in Sec. III B.

Finally, at LIGO Hanford, another source of environmental noise, ground tilt induced by wind on the buildings,

was mitigated by installing wind fences that reduce the wind velocity at the end stations [607]. This has been shown to lower ground tilt. The effect on data quality and duty cycle is still being investigated.

While the Hanford and Livingston detectors are nominally the same design [1], differences in environment and implementation result in different sensitivity during O3b. Hanford has more unexplained noise from 30 to 100 Hz and more angular control noise below 30 Hz. The higher noise above 430 Hz in the Hanford spectrum is due to lower optical power causing increased shot noise as well as higher frequency-dependent losses that degrade the squeezing above the interferometer bandwidth [608].

## 2. Virgo Observatory

The one-month commissioning break between the two observing periods was used to get a better understanding of the Virgo sensitivity and of some of its main limiting noises. Throughout O3, work was continuously carried out to improve the Virgo sensitivity in parallel with the ongoing data taking. Dedicated tests were made during planned breaks in operation (commissioning, calibration, and maintenance), and in-depth data analysis of these tests was performed between breaks to ensure continual improvement. This effort culminated during the last three months of O3b, as shown by the step in the BNS inspiral range evolution in the left panel of Fig. 3, and by the bimodal BNS inspiral range distribution in the right panel.

The most significant change to the Virgo configuration between O3a and O3b was the increase of the input power from 18 to 26 W. As for the LIGO detectors, we find that the optical losses of the arms increase following the increase of the input power. The presence of absorbing points on the arm-cavity mirrors is suspected [599], and mitigation strategies will be implemented before O4.

The squeezing system in the Virgo interferometer was implemented before the start of O3a, and squeezing injection was maintained during the whole O3, with a gain in sensitivity at high frequency [602,609]. Prior to the start of O3a, new high-quantum-efficiency photo-diodes were installed at the output (detection) port of the
interferometer. These diodes increased the electronics noise at low frequency, but were improved at the end of January 2020 during a maintenance period, by replacing preamplifiers. The electronic noise disappeared completely, leading to a BNS inspiral range gain of approximately 2 Mpc.

Shortly thereafter, an extended period of continuous and stable control of the Virgo detector allowed improvement to the performance of the etalon feedback system designed to reduce the residual asymmetry between the optical line-widths of the interferometer arm cavities [610]. To compensate for this asymmetry, the input mirrors of the Virgo Fabry-Perot cavities have parallel faces that create an optical resonator (the etalon) inside the substrate. To remain close to the optimized working point, it is necessary to reduce the temperature variations of the substrate by using heating belts in the input test-mass towers. The implemented feedback requires hours to reach equilibrium, but has a temperature accuracy of 6 mK, about 2% of a full etalon fringe (532 nm). The BNS inspiral range improvement from this etalon feedback control is approximately 2–3 Mpc.

During the same period, it was discovered that some channels used as input for the GW strain channel reconstruction were numerically limited by quantization errors. Changing their storage from float to double precision led to an immediate gain of approximately 2 Mpc for the BNS inspiral range.

Finally, in the period between the end of January to the beginning of February 2020, the alignment was improved for the injection of the squeezed light into the interferometer [602,609], a critical parameter of the low-frequency sensitivity. By mitigating scattered-light noise, the BNS inspiral range increased by approximately 1–2 Mpc.

All these quasisimultaneous hardware and software improvements led to a significant increase in the BNS

inspiral range visible in the data after 28 January 2020 (Fig. 3, left panel). The median range improved from 49 Mpc (before 28 January 2020) to 56 Mpc (after 28 January 2020). The Virgo sensitivity improved over the whole frequency range, with a larger improvement below about 300 Hz, around the minimum of the sensitivity curve and at lower frequencies.

## APPENDIX C: DATA-QUALITY METHODS

Information about the data quality of the detectors is repackaged into products used by astrophysical analyses, including data-quality flags, gating, and iDQ glitch likelihoods, as introduced and discussed below. Including this information in searches, as summarized in Table IX for each offline analysis, increases the total number of detectable signals [63,611,612]. The most egregious periods of light-scattering glitches in the LIGO detectors are vetoed from the astrophysical analyses through a combination of these veto products, but the rate of scattering glitches was so high in the beginning of O3b, especially in LIGO Hanford data, that current methods cannot effectively exclude these glitches without losing large stretches of data [63].

Data-quality flags are lists of time segments that identify the status of the detectors or the likely presence of a particular instrumental artifact. These flags are broken into three categories based on the severity of the data-quality issue and how the flag was designed [63,96,612]. The amount of time removed by data-quality flags in each detector is typically of order 1%. Table IX shows the cumulative fractional time removed by each category during O3b. The fractional time removed by individual data-quality flags can be found in a summary of flags

<table><caption>TABLE IX. Top: data-quality products used for noise mitigation by each offline search pipeline. Products listed here are publicly available from GWOSC [33]. Most analyses employ additional internal noise mitigation methods, including gating [79,83,93,110,613]. Bottom: the percent of single-detector time removed by each of the same veto categories for each detector during O3b. Veto time values for LIGO Hanford and LIGO Livingston are reproduced from studies of O3 detector characterization [63]. Three center dots (...) in a data-quality product's column indicates that it is not produced for the relevant detector, except for iDQ output; iDQ has no associated removed time as it is incorporated directly into the search-pipeline ranking statistic [611]. The listed removed time is in addition to the downtime associated with one or more detectors not being in a nominal observing state, as described in Sec. II, which is common to all searches.</caption><thead><tr><th>Search pipeline</th><th>Category 1</th><th>CBC category 2</th><th>Burst category 2</th><th>Burst category 3</th><th>Gating</th><th>iDQ</th></tr></thead><tbody><tr><td>cWB</td><td>✓</td><td>✗</td><td>✓</td><td>✓</td><td>✗</td><td>✗</td></tr><tr><td>GstLAL</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td><td>✓</td></tr><tr><td>MBTA</td><td>✓</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td></tr><tr><td>PyCBC</td><td>✓</td><td>✓</td><td>✗</td><td>✗</td><td>✓</td><td>✗</td></tr></tbody></table><table><thead><tr><th>Detector</th><th>Category 1</th><th>CBC category 2</th><th>Burst category 2</th><th>Burst category 3</th><th>Gating</th><th>iDQ</th></tr></thead><tbody><tr><td>LIGO Hanford</td><td>0.30%</td><td>0.02%</td><td>0.52%</td><td>0.41%</td><td>0.01%</td><td>...</td></tr><tr><td>LIGO Livingston</td><td>1.68%</td><td>0.28%</td><td>0.50%</td><td>0.17%</td><td>0.01%</td><td>...</td></tr><tr><td>Virgo</td><td>0.21%</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>
applied during O3 for LIGO and Virgo [614,615]. Category 1 flags indicate time periods where data should not be analyzed due to either incorrect configuration of the detector, operator error, or egregious data-quality issues. All GW searches uniformly use category 1 flag information to exclude these time periods. Category 2 flags are designed to indicate segments that are predicted to contain non-Gaussian artifacts likely to trigger GW searches based on information from auxiliary channels [63]. While data during category 2 flags is still used in analyses to compute estimates of the power spectral density (PSD), searches that use category 2 vetoes do not consider any triggers during these time periods in estimates of significance. The set of category 2 flags that are used in analyses is different between the CBC analyses that use waveform templates and the Burst analyses that are more waveform agnostic. Similar to category 2 flags, category 3 flags are used to indicate periods of transient noise, but are constructed using estimates of statistically significant correlations between glitches in auxiliary channels and behavior of GW detector data [420]. Category 3 flags are produced only for use by the Burst analysis cWB.

The gating method removes short-duration artifacts from the data by smoothly rolling the data containing the artifact to zero with an inverse window function, as employed for LIGO data during previous observing runs [63]. The gating data product referenced in Table IX and available from GWOSC [33] was generated using times corresponding to a loud excursion in the data identified with auxiliary channel information. Most transient search algorithms also employ internal gating methods to exclude noise transients from analysis based only on the amplitude of the glitch.

The iDQ glitch likelihood uses machine learning to predict the probability that a non-Gaussian transient is present in detector data based only on information from auxiliary channels [421]. This likelihood is used by GstLAL as a part of the search-pipeline ranking statistic to penalize triggers near periods of high iDQ likelihood [611]. As shown in Table IX, GstLAL incorporates iDQ glitch likelihood information in lieu of applying category 2 or 3 data-quality flags.

Astrophysical analyses performed online use different data-quality products from those listed in Table IX. Online data-quality products describe the state of the detectors and the data using only products available within the low latency needed for the online search analyses and the sending of public alerts (as detailed in Appendix A). For example, the category 2 and 3 data-quality flags used by offline searches are often informed by follow-up investigations over the scale of weeks or months after data are initially collected. Table X lists the state vector and data-quality products available online, and which searches use each of these. Online data-quality products used in O3, including online detector state vectors, the LIGO data-quality vector, search-specific online Virgo vetoes, Virgo online category 1 products, and an online version of gating, are described in detail in related papers about LIGO [63] and Virgo detector characterization [77].

After the event-validation procedures described in Sec. III B, we assess whether excess power present within the target analysis time of any candidate is sufficiently nonstationary to require mitigation [44,617]. We compare the variance of the noise PSD in each identified time-frequency region for consistency with Gaussian noise. Time-frequency regions inconsistent with Gaussian noise ($p < 0.01$) are deglitched, as described below, before source-parameter estimation. Details of the candidates requiring mitigation are given in Appendix E 1.

The majority of glitch-subtracted data discussed in Appendix E 1 were produced with the BayesWave algorithm [377,379]. BayesWave models localized excess power as a sum of sine-Gaussian wavelets, using a multicomponent model that simultaneously fits signals, glitches, and the PSD of the Gaussian noise component using a transdimensional Bayesian inference, wherein the number of model components (wavelets, spectral lines, and spline control points for the smooth portion of the PSD) is allowed to vary, in addition to the parameters that describe each component.

The signal model reconstructs the plus and cross polarization states of a GW signal as a sum of wavelets, which are coherently projected onto the detector

<table><caption>TABLE X. State information and data-quality products used for noise mitigation by each online search pipeline. For each detector, the state vector defines the times the detector is online and the data are ready for analysis. The LIGO data-quality vector and Virgo online category 1 products flag known instrument artifacts during observing mode [63,616]. Information from online data-quality products is available in a different form for offline searches, e.g., the category 1 and 2 data-quality products, as part of the products listed in Table IX. Most analyses employ additional internal noise mitigation methods, including gating [79,83,93,110,613].</caption><thead><tr><th>Search pipeline</th><th>State vector</th><th>LIGO data-quality vector</th><th>Virgo online category 1</th><th>Virgo PyCBC veto</th><th>Online gating</th></tr></thead><tbody><tr><td>cWB</td><td>✓</td><td>✓</td><td>✓</td><td>✗</td><td>✗</td></tr><tr><td>GstLAL</td><td>✓</td><td>✓</td><td>✓</td><td>✗</td><td>✗</td></tr><tr><td>MBTAOnline</td><td>✓</td><td>✓</td><td>✓</td><td>✗</td><td>✗</td></tr><tr><td>PyCBC Live</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✗</td></tr><tr><td>SPIIR</td><td>✓</td><td>✓</td><td>✓</td><td>✗</td><td>✓</td></tr></tbody></table>
network [379]. We use the waveform reconstruction produced by BayesWave in the waveform consistency tests as discussed in Sec. VI. The glitch model reconstructs noise transients separately in each detector. The spectral model adjusts to take into account the power that gets assigned to the signal and glitch models. Central to the BayesWave approach is that the model dimension is not fixed, with both the number of wavelets and their parameters explored using a transdimensional reversible jump Markov-chain Monte Carlo algorithm [618]. Louder signals generally demand more wavelets. In the case of CBC signals, high-mass, short-duration signals are generally reconstructed with fewer wavelets than low-mass, longer-duration signals.

The natural parsimony of Bayesian inference works to ensure that any coherent signal power is assigned to the signal model, while any incoherent noise transients are assigned to the glitch power, since fitting the data with a coherent model requires fewer parameters than fitting the data in each detector independently. Thus, this method allows us to remove glitches even if they overlap with a GW signal [126,379]. Going forward, it may be desirable to perform the glitch fitting and PSD estimation in concert with the CBC parameter estimation [162]. In the current analysis, the BayesWave algorithm is used to produce cleaned data and point estimates of the PSD that are then used in source-parameter estimation (Appendix E).

<figure><img src="image_18.png" /><figcaption>FIG. 15. A spectrogram [73] of LIGO Livingston data prior to the estimated merger time of GW200115_042309. The top plot shows the untreated data and the bottom shows the data with some excess power due to fast scattering subtracted [379]. The estimated signal track is represented as an orange line. A white dashed line shows the lower frequency used for source-parameter estimation for the original GW200115_042309 inference ($f_{low}$ = 25 Hz) [8].</figcaption></figure>

An example of glitch subtraction by the BayesWave algorithm is illustrated in Fig. 15 for the case of analyzing GW200115_042309. The glitches removed here are fast scattering, one of the most common glitches observed in O3b LIGO Livingston data, as described in Sec. III B [63,70].

The mitigated data discussed in Appendix E 1 for GW200129_065458 are produced with the `gwsubtract` algorithm [44], which employs linear subtraction [59,619]. We use a photodiode monitoring an element of the LIGO Livingston detector's input optics (L1:LSC-POP_A_RF9_I_ERR_DQ) identified [620] as a linear witness of the glitch. The time of the subtracted glitch is also identified as correlated with an auxiliary witness channel by a CBC category 2 data-quality flag [59] defined as flag 1.24 (45 MHz sideband fluctuations) in the O3 LIGO data-quality flag summary [614].

In order to assess the efficacy of glitch subtraction by either method described above for O3b candidates, we compare the stationarity of the glitch-subtracted data within the targeted time-frequency window to Gaussian noise. Glitch-subtracted data consistent with Gaussian noise are deemed sufficiently stationary for parameter estimation.

Uncertainties related to the glitch modeling are not accounted for in source-parameter estimation. To do so would require glitches to be modeled simultaneously with inference of the source properties. Analyses estimating both the properties of glitches and signals have found that the glitch modeling uncertainty may impact the inferred source properties in specific parts of the parameter space [162,621,622]. However, joint glitch and source inference has not yet been incorporated into the inference algorithms used here. Both of the glitch-subtraction methods used in this work have different associated uncertainties, and may work better in different circumstances; for example, BayesWave works well when its coherent wavelet analysis accurately models the glitch, and `gwsubtract` works well when there is a reliable witness channel [44].

## APPENDIX D: CANDIDATE-IDENTIFICATION METHODS

### 1. GstLAL

The `GstLAL` pipeline [78–81,623,624] uses matched filtering in the time domain to detect triggers and coincidences. We model signals and search for them in the data using the same template bank as for the GWTC-2 analysis [3]. The template bank covers waveforms with redshifted total masses from $2M_\odot$ to $758M_\odot$. The spins are assumed to be parallel (aligned or antialigned) to the orbital angular momentum; the spin magnitudes range from -0.05 to 0.05 for components with redshifted masses $<3M_\odot$, and from -0.999 to 0.999 for components with redshifted masses $>3M_\odot$. The template bank is constructed using a stochastic placement method in five different regions of the parameter space that are the same as those defined for the GWTC-2
analysis [3]. The SEOBNRv4_ROM waveform approximant [625] is used for templates with chirp mass $\ge 1.73M_\odot$; this waveform is a frequency-domain reduced-order model [626] of the time-domain inspiral-merger-ringdown model SEOBNRv4 which models quasicircular, nonprecessing BBHs based upon the effective-one-body (EOB) equations of motion [625]. The TaylorF2 waveform approximant [98,627–635] is used for lower-mass systems; this waveform is a frequency-domain, inspiral-only model of aligned-spin CBC systems built from closed-form PN approximations. The template bank is constructed such that any template in the continuous parameter space is certain to match at least one template in the discrete space to greater than a chosen minimum match, where the match used is that given in Eq. (6), maximized over the phase and time of coalescence. The value of the minimum match is chosen to ensure that the SNR loss due to the templates not exactly matching the signals is acceptable while keeping the total number of templates small enough to be computationally feasible. The minimum match is dependent on the region of the parameter space, but is never smaller than 0.97 [3].

Triggers are defined by maximizing the matched-filter SNR for each template, in each detector, over 1-s time windows [78]. We use a SNR threshold of $\rho > 4.0$ to define triggers. Triggers from the same template that are time coincident in multiple detectors are grouped together to form events [78]. The GstLAL analysis uses single-detector triggers from HL coincident time (when either HL or HLV were operating) to estimate background statistics in bins according to template mass. This is due to the low probability of a real signal appearing above threshold in only LIGO Hanford or LIGO Livingston when both detectors are operating. Triggers from single-detector time, or times when only HV or Livingston-Virgo (LV) were operating, are excluded from the background estimation to avoid significant contamination by true astrophysical signals.

The likelihood ratio is informed by observables such as the matched-filter SNR from each detector, detector sensitivities at the time of coincidence, as well as the output of signal-based-veto tests, and time and phase differences between triggers [79]. The events are ranked by the likelihood-ratio statistic which compares the probability in the signal hypothesis of finding the given observables to the probability of the same observables in the noise hypothesis. In addition, the likelihood ratio includes a term from iDQ [611], a statistical inference framework that identifies short-duration non-Gaussian artifacts in the strain data [421] (described in Appendix C). As discussed in the GWTC-2.1 paper [4], iDQ time series were regenerated offline using an acausal binning scheme and a larger set of auxiliary witness channels, making its data products more sensitive in identifying noise artifacts compared to their online counterpart. An increased sampling rate in the offline configuration also allowed for better resolution of

short-duration glitches. Because of these changes, iDQ had an improved performance in identifying glitches. Accordingly, starting in O3b, iDQ now has the capability to increase the significance of candidates during times in which no noise artifacts are identified: Whereas in the previous procedure used for GWTC-2 [3], the iDQ term in the GstLAL likelihood ratio was restricted to be positive, so that it could only decrease the significance of candidates [611], it may now be either positive or negative. Additionally, iDQ is now applied to both coincident and single-detector candidates.

Since O2, the GstLAL pipeline has allowed for the possibility of single-detector candidates [79]. This includes two cases: triggers from a time when only one detector was operational, and noncoincident triggers from one detector even when multiple detectors were operational. Single-detector candidates are required to pass the SNR threshold as well as a preliminary likelihood-ratio threshold. However, single-detector candidates are downweighted with a singles penalty in the likelihood-ratio statistic, depending on the detector in which it was observed and the sensitivities of the detectors which were on at the trigger time [4].

## 2. MBTA

MBTA [82,83] uses a template bank covering binaries with redshifted component masses ranging from $1M_\odot$ to $195M_\odot$, with the additional constraints that the maximum total mass is $200M_\odot$, and if the secondary object has a mass lower than $2M_\odot$, then the maximum mass of the primary object is $100M_\odot$. Objects are assumed to have spins parallel to the orbital momentum with maximum dimensionless values 0.05 if their masses are below $2M_\odot$, and 0.997 otherwise. The templates are generated in the time domain, using the SpinTaylorT4 waveform approximant [631,632,634,636–640] if both objects have masses below $2M_\odot$, and the SEOBNRv4 waveform [625] otherwise. The SpinTaylorT4 waveform is an inspiral-only, time-domain model for CBC systems based on the PN equations of motion, while SEOBNRv4 is a full inspiral-merger-ringdown waveform appropriate for BBHs. The template bank is produced using a stochastic placement method.

The MBTA pipeline starts with a preprocessing step, where data are downsampled then gated at (externally or internally) identified times of bad data quality. To mitigate safety issues in the gating procedure, a subset of the template bank is also analyzed without applying the gating procedure, albeit with higher SNR thresholds ($\rho > 9.5$ in Hanford, 11.3 in Livingston, and 12 in Virgo). MBTA splits the parameter space into three regions treated as independent searches. The regions can be considered to cover the BNS, NSBH, and BBH source types, although the transition between NS and BH is conservatively taken to be $2M_\odot$ (to allow for any heavier object to possibly have high spin) [4]. Single-detector triggers are ranked according to a
statistic based on the matched-filter SNR modified to take into account the consistency with an astrophysical signal (quantified from the quadratic average of the difference between the SNR time series around its maximum and the template autocorrelation) and the local data quality (quantified from the overall pipeline response). Coincidences are ranked according to a statistic based on the quadratic sum of the single-detector triggers ranking statistics modified to take into account the consistency of some parameters across the various detectors.

MBTA initially assigns a FAR to events depending on the coincidence type (whether HL, HV, LV, or HLV depending on which detectors provided a trigger), and the parameter-space region. The FAR is then modified to take into account trials factors from the various coincidence types and regions. For double coincidences, the FAR at a given ranking statistic threshold is estimated from the rate of false coincidences (built from single-detector triggers in that region) that are as loud or louder. Single-detector triggers that are known to be part of foreground coincidences with a combined ranking statistic above 10 are excluded from this process, as such statistic values typically correspond to low FARs (typically less than $0.2 \text{ yr}^{-1}$ for HL coincidences) indicating a probable astrophysical origin. The FAR for triple coincidences is derived from that of double coincidences. Equal trials factors are applied for the three parameter-space regions, whereas for coincidence types, trials factors are applied according to the likelihood of astrophysical sources being detected as coincidences of each type, considering the relative detector sensitivities.

### 3. PyCBC

We employ two offline PyCBC configurations in this work [23,84–88,641]. The first, the PyCBC-broad analysis, is designed to search for as many different types of signal as possible, and probes a wide range of masses and spins. Following previous searches [3,4,17,19], we also perform an analysis focusing on the BBH region of the parameter space in which we have seen most of our signals so far, making use of a population prior [642]. This second approach is the PyCBC-BBH analysis.

The PyCBC-BBH analysis focuses on a region ranging in primary component mass from $5M_{\odot}$ to $350M_{\odot}$, with mass ratios from 1/3 to 1, and aligned, equal component spins ranging from -0.998 to 0.998. The PyCBC-broad template bank covers a similar parameter space as the GSTLAL template bank, but with a few significant changes. Both the PyCBC-broad and PyCBC-BBH analyses use the SEOBNRv4_ROM [625] waveform approximant for templates with total mass above $4M_{\odot}$, and TaylorF2 [98,627–635] for lower-mass systems. The templates within the template bank are placed using a hybrid geometric-random method [643,644], and no template is used that has a duration of less than 0.15 s [645], meaning there is an upper limit on the mass of the systems. If this duration limit is relaxed and additional vetoes on transient data

artifacts are applied, higher sensitivity to high-mass systems may be obtained [26,646].

Both the PyCBC-broad and PyCBC-BBH analyses use data from all detectors, searching for coincident triggers in two or more detectors. For each coincident event, we calculate a ranking statistic which is compared to the background to calculate the significance, finally combining the significances from each possible combination of triggers from the available detectors (the coincidence type) into a single result.

The search in the three-detector network is done by performing coincident searches in each coincidence type, and then combining FAR depending on the available coincident combinations. For example, if an event is seen as a HL coincidence, the ranking statistic would be calculated, and the FAR estimated by counting higher-ranked events in a time-shifted background. If the Virgo detector is observing, then the FAR from the detected event would be added to the FAR at that ranking statistic from each of HV, HL, and HLV backgrounds. This method means that we effectively apply a trials factor where it is needed, but not when the coincidence type in which the candidate was found is the only one available such that a trials factor would be inappropriate.

The PyCBC pipelines use a ranking statistic based on the ratio of the expected signal rate and the measured noise rate [17,88]. This choice of ranking statistic has two consequences. First, we are able to incorporate more information about the detectors into our assessment of whether an apparent signal is real or not. For example, we now account for the sensitive volume of the detector network at the time of a candidate and combine the single-detector rates of noise triggers with the time window for coincidences in order to estimate the coincident-trigger rate. Second, we are able to directly combine FARs by summing the FARs at the ranking statistic of the event for each coincidence type available at the time; by adding the FARs rather than using a trials factor, we take into account the vastly different FARs for different coincidence types at the same ranking statistic.

The PyCBC-BBH ranking statistic uses a chirp-mass weighting designed to approximately model the BH population. In previous analyses [17], this weighting took a different functional form above a template chirp mass of $40M_{\odot}$, suppressing higher-mass triggers; however, in this analysis, due to an omission in implementation, the same functional form is continued over all templates. This change results in a higher background noise level than expected due to triggers in high-mass templates caused by glitches, potentially reducing the sensitivity of the search. From the sensitivity studies in Sec. IV E 1, we see that the sensitivity reduction is likely to be small.

Recent alterations to the PyCBC analysis allow the use of graphics processing unit (GPU) cores or distributed computing through the Open Science Grid [647,648] in order to perform matched filtering more quickly.

The PyCBC analysis used in this work did not analyze single-detector signals, though recent work allows this
feature [21,128]. Usually, triggers from significant signals are removed from the background of lower-ranked events within the analysis, in a process called hierarchical removal [649], but as we do not calculate single-detector significance, we have no metric by which to remove these triggers, and so signal triggers can remain in the background. As a result, these loud triggers from signals can match noise triggers in the time-shifted background and cause an excess of highly ranked background events. In order to prevent the contamination of the background, PyCBC analyses are performed twice: first with all triggers in place, and then again with the triggers removed from catalog candidates that do not form coincidences in the preliminary analysis. To ensure that this process matches the usual hierarchical removal procedure, we use the list of candidates from other analyses for this catalog that have a FAR of less than $10^{-2}$ yr$^{-1}$, and compare these to the list of coincident events in the PyCBC analyses. If no coincident event (of any significance) is found in the PyCBC pipeline, then a window of 1 s either side of each event is removed. The triggers removed from the background in the PyCBC-broad pipeline are from around GW200112_155838 and GW200202_154313, and from the PyCBC-BBH pipeline we remove the triggers from around GW200112_155838. The sensitive hypervolume estimates of Sec. IV E 1 use the analysis with the triggers from single-detector events removed. Only a small subset of the analysis chunks are significantly affected by this change, and this effect is particularly muted at the threshold we consider for $\langle VT \rangle$ estimates [21].

In addition to the offline analyses described above, we also use PyCBC Live [613,650] to search for signals in low latency. The PyCBC Live algorithm uses the data and data-quality information that are available in low latency (as described in Appendix C) without human vetting. PyCBC Live uses a more computationally simple ranking statistic than the one used in offline analyses. This simpler ranking statistic is used in order to maintain speed in a low-latency environment and does not contain all of the information used in the offline statistic. The reduced $\chi^2$-reweighted SNR [23] and a sine-Gaussian veto [402,651] are used to assess significance of single-detector triggers. These single-detector triggers are then tested for coincidence, and the coincident ranking statistic is calculated. The ranking statistic is compared to the time-shifted background from five hours of data to estimate FAR.

## 4. SPIIR

The SPIIR pipeline [91–93] ran as an online low-latency modeled coherent search. SPIIR is a time-domain equivalent to matched filtering that uses infinite impulse response filters [93,652] to approximate waveforms with high accuracy and, in theory, constructs the SNR at zero latency. In O3 the pipeline operated in two low-latency, parallel modes: one to search using data from the two LIGO

detectors, and another using data from all three detectors. SPIIR searches templates with primary component mass ranging from $1.1M_\odot$ to $100M_\odot$, a subset of the GstLAL template bank [93]. For online low-latency analyses, this method is more computationally efficient than traditional Fourier methods, with latency 7–10 s in O3 [93]. The filtering process [653–655] and coherent candidate selection [91] are accelerated using GPUs.

The pipeline ranks the triggers by a combination of the coherent network SNR and a $\chi^2$-distributed signal-consistency statistic from the individual detectors [78,93]. It computes the background of the search by performing 100 time shifts per foreground trigger with SNR greater than 4. The $k$-nearest-neighbors technique is used to estimate the significance for triggers [93]. The FAR for each trigger is estimated over three timescales (two hours, one day, and one week) of collected background triggers for robustness, with the most conservative used for candidates.

## 5. cWB

The cWB pipeline detects and reconstructs transient signals with minimal assumptions [60,89,107–109] by coherently analyzing data from multiple observatories. The sensitivity of cWB approaches that of matched-filter methods for coalescing stellar-mass BBHs with high chirp masses [26,656], such that it can detect high-mass CBC sources, and also sources that are not well represented in current template banks such as eccentric systems or large mass asymmetry, precessing BBH systems [378]. It was used in previous CBC searches by the LVK [3,12,14,657].

The cWB algorithm analyzes whitened data using the Wilson-Daubechies-Meyer wavelet transform [89,108] to compute a time-frequency representation. The algorithm selects excess-energy data in the time-frequency representation and clusters them to define a trigger. Next, it identifies coherent signal power with the constrained maximum-likelihood method [60], and reconstructs the source sky location and the signal waveforms.

After identifying clusters of coherent data, cWB outputs several statistics. These include the total cluster energy for each detector, the coherent energy $E_c$ of the reconstructed signal obtained by cross-correlating the normalized signal waveforms reconstructed in different detectors, the residual noise energy $E_n$ estimated after the reconstructed waveforms are subtracted from the data, and the estimate of the coherent SNR in each detector. The residual noise energy is used to form a chi-squared statistic $\chi^2 = E_n/N_{DF}$, where $N_{DF}$ is the number of independent wavelet amplitudes describing the trigger. We estimate the signal SNRs from the reconstructed waveforms. Then, by combining the SNRs of the individual detectors, we calculate the network SNR. The network correlation coefficient $c_c = E_c/(E_c + E_n)$ is another derived statistic that compares coherent and null energies; it approaches 1 when coherence is high, as expected for real signals. The cWB detection statistic is
$\eta_c \propto [E_c/ \max(\chi^2, 1)]^{1/2}$, where the $\chi^2$ correction is applied to reduce the contribution of non-Gaussian noise.

For robustness against glitches and to reduce the FAR of the pipeline, cWB uses signal-independent vetoes, which include Burst category 2 data-quality flags in the processing step and category 3 in the postproduction phase [420,658]. To further reduce background, the cWB analysis applies cuts based on the network correlation coefficient $c_c$ and on the $\chi^2$, and employs signal-dependent vetoes based on basic properties of the time-frequency evolution of CBC signals [111,659].

A generic search for CBC systems covers a large parameter space, and it is not possible to design a search that is optimized for all such systems because of the wide frequency range in which the signals fall. With the setup used for this catalog, cWB can reconstruct GW signals with durations up to a few seconds in the detectors' frequency range, which makes it better suited to identify BBH signals than longer NSBH or BNS signals. A CBC signal has a peak frequency inversely proportional to the redshifted total mass, so that less massive binary systems merge at higher frequencies, while more massive systems merge at lower frequencies. Therefore, just as for the GWTC-2 analysis [3], the cWB analyses in this catalog are performed with two pipeline configurations targeting the detection of high-mass ($f_c < 80$ Hz) and low-mass ($f_c > 80$ Hz) BBH systems. These configurations use different signal-dependent vetoes defined a priori to alleviate the large variability of non-stationary noise in the detectors' bandwidth.

We estimate the FAR of triggers by time shifting the data of one detector with respect to the other in each detector pair, with time lags so large (typically multiples of 1 s) that actual astrophysical signals are excluded, and repeating this for a large number of different time lags over a total time $T_{bkg}$ which is of the order of $10^3$ yr. We count the number of triggers $N_{bkg}$ due to background noise having a SNR (or another similar ranking statistic) that is at least as large as that of the trigger, and we compute the FAR as the $N_{bkg}$ divided by $T_{bkg}$ [660].

The detection significance of a trigger identified by either pipeline configuration in a single frequency range is determined by its FAR measured by the corresponding cWB configuration. In the end, each configuration reports the selected triggers and their FAR. Whenever the low-mass and high-mass configurations overlap, the trials factor of two (the Bonferroni adjustment for the false alarm probability [661]) is included to determine the final FAR [184].

The cWB algorithm can work with arbitrary detector networks, although the cWB analysis presented in this catalog is restricted to the HL, HV, and LV pairs. The HLV network is not included here because it does not improve the significance of the cWB candidates for the current sensitivity of the detector network [31]. Thanks to their near alignment, the two LIGO detectors select a well-defined GW polarization state, and cWB can efficiently

exploit coherence to mitigate their glitches and make the remaining noise close to Gaussian. Conversely, the orientation of the Virgo detector differs considerably from that of the LIGO detectors so that, at the current sensitivity level, glitches in Virgo data cannot be mitigated as efficiently, and this reduces the discriminating power of current cWB HLV analyses with respect to HL analyses.

## 6. Search results

In Sec. IV D, we presented the $p_{astro}$, FAR, and network SNR of candidates with CBC $p_{astro} > 0.5$ or FAR $< 2.0$ yr$^{-1}$ in Tables I and II, respectively. Here, we additionally provide the single-detector SNRs of each candidate in Table XI. The single-detector SNRs are used as an initial criterion by pipelines to define triggers and determine coincidences, and therefore are an important component in calculating the significance of a detection candidate. The detectors listed in Table I are those that were operating at the time of each candidate, but whether a candidate was missed or found in a particular detector depends on the matched-filter SNR found by each pipeline in the detector's data. In particular, each of the single-detector candidates, GW200112_155838, GW200302_015811, and GW200105_162426, were found during times when either LIGO Livingston or LIGO Hanford were operating simultaneously with the Virgo detector. However, Table XI shows that these were still classified as single-detector candidates since in each case the SNR in Virgo was <4.0. Regardless of the number of detectors used for detection, data from all operating detectors are used for inference of the source parameters (described in Appendix E).

Candidates found by multiple analyses typically have comparable SNRs, but we do not expect the values to be identical because of differences in the template banks and how the pipelines select the most significant template when identifying a candidate. The most noticeable difference is in the Livingston SNR for GW200129_065458, as discussed in Sec. IV D 3; this is a result of the different analyses' handling of data-quality flags.

## 7. Search sensitivity and probability of astrophysical origin

To assess search sensitivity, we inject simulated signals into the data, and attempt to identify them with each search analysis. The details of the injected populations (which are the same as used for GWTC-2.1 [4]) are given in Table XII, and the injected distributions over redshift are defined assuming a flat $\Lambda$-cold-dark-matter cosmology such that

$$p(z) \propto \frac{dV_c}{dz} (1+z)^{\kappa-1}, \qquad (\text{D1})$$

where $V_c$ is the comoving volume (see Appendix E for the assumed cosmology [662]). These injected populations are
<table><caption>TABLE XI. Individual-detector SNRs for all candidates in Tables I and II. LIGO Hanford, LIGO Livingston, and Virgo are indicated by H, L, and V, respectively. Numbers in italics indicate where a candidate is identified with probability of astrophysical origin $p_{astro} < 0.5$. Three center dots (· · ·) indicate where no significant trigger is identified by a search analysis.</caption><thead><tr><th rowspan="2">Name</th><th colspan="2">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>H</th><th>L</th><th>H</th><th>L</th><th>V</th><th>H</th><th>L</th><th>V</th><th>H</th><th>L</th><th>V</th><th>H</th><th>L</th><th>V</th></tr></thead><tbody><tr><td>GW191103_012549</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>6.5</td><td>6.3</td><td>...</td><td>6.3</td><td>6.8</td><td>...</td><td>6.2</td><td>6.9</td><td>...</td></tr><tr><td>GW191105_143521</td><td>...</td><td>...</td><td>5.8</td><td>7.6</td><td>2.8</td><td>6.1</td><td>8.2</td><td>3.1</td><td>5.9</td><td>7.8</td><td>...</td><td>5.9</td><td>7.8</td><td>...</td></tr><tr><td>GW191109_010717</td><td>9.8</td><td>12.1</td><td>8.5</td><td>13.3</td><td>...</td><td>8.6</td><td>12.6</td><td>...</td><td>8.7</td><td>9.9</td><td>...</td><td>9.0</td><td>11.3</td><td>...</td></tr><tr><td>GW191113_071753</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>6.3</td><td>6.4</td><td>2.2</td><td>6.3</td><td>5.4</td><td>...</td><td>6.1</td><td>5.9</td><td>...</td></tr><tr><td>GW191118_212859</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>5.2</td><td>6.1</td><td>...</td><td>5.5</td><td>7.2</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW191126_115259</td><td>...</td><td>...</td><td>5.7</td><td>6.5</td><td>...</td><td>5.7</td><td>6.3</td><td>...</td><td>5.8</td><td>6.2</td><td>...</td><td>5.8</td><td>6.2</td><td>...</td></tr><tr><td>GW191127_050227</td><td>...</td><td>...</td><td>6.8</td><td>6.7</td><td>4.0</td><td>6.7</td><td>6.4</td><td>3.2</td><td>7.0</td><td>6.4</td><td>...</td><td>6.1</td><td>6.2</td><td>...</td></tr><tr><td>GW191129_134029</td><td>...</td><td>...</td><td>8.8</td><td>10.0</td><td>...</td><td>8.5</td><td>9.4</td><td>...</td><td>8.6</td><td>9.6</td><td>...</td><td>8.6</td><td>9.6</td><td>...</td></tr><tr><td>GW191204_110529</td><td>...</td><td>...</td><td>4.6</td><td>7.8</td><td>...</td><td>5.4</td><td>6.0</td><td>...</td><td>5.0</td><td>7.4</td><td>...</td><td>5.0</td><td>7.4</td><td>...</td></tr><tr><td>GW191204_171526</td><td>9.0</td><td>14.5</td><td>8.9</td><td>12.8</td><td>...</td><td>10.0</td><td>13.8</td><td>...</td><td>9.8</td><td>13.8</td><td>...</td><td>9.8</td><td>13.8</td><td>...</td></tr><tr><td>GW191215_223052</td><td>6.6</td><td>7.3</td><td>7.0</td><td>7.8</td><td>3.0</td><td>6.7</td><td>7.9</td><td>3.0</td><td>7.2</td><td>7.5</td><td>...</td><td>7.0</td><td>7.5</td><td>...</td></tr><tr><td>GW191216_213338</td><td>...</td><td>...</td><td>17.8</td><td>...</td><td>5.6</td><td>17.1</td><td>...</td><td>5.4</td><td>17.6</td><td>...</td><td>5.2</td><td>17.6</td><td>...</td><td>5.2</td></tr><tr><td>GW191219_163120</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>4.8</td><td>7.5</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW191222_033537</td><td>7.9</td><td>7.8</td><td>8.8</td><td>8.2</td><td>...</td><td>8.3</td><td>7.0</td><td>...</td><td>8.4</td><td>7.9</td><td>...</td><td>8.4</td><td>7.9</td><td>...</td></tr><tr><td>GW191230_180458</td><td>7.4</td><td>7.1</td><td>7.2</td><td>7.0</td><td>1.9</td><td>7.4</td><td>5.9</td><td>2.4</td><td>7.2</td><td>6.2</td><td>...</td><td>7.3</td><td>6.6</td><td>...</td></tr><tr><td>GW200105_162426</td><td>...</td><td>...</td><td>...</td><td>13.6</td><td>2.6</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200112_155838</td><td>...</td><td>...</td><td>...</td><td>17.5</td><td>2.1</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>...</td><td>...</td><td>6.7</td><td>8.9</td><td>2.8</td><td>6.6</td><td>8.6</td><td>2.6</td><td>6.3</td><td>8.8</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>200121_031748</td><td>...</td><td>...</td><td>8.2</td><td>...</td><td>4.0</td><td>9.5</td><td>...</td><td>4.9</td><td>...</td><td>...</td><td>...</td><td>7.3</td><td>...</td><td>4.0</td></tr><tr><td>GW200128_022011</td><td>6.7</td><td>5.7</td><td>7.4</td><td>6.9</td><td>...</td><td>6.9</td><td>6.4</td><td>...</td><td>7.0</td><td>6.9</td><td>...</td><td>7.2</td><td>6.9</td><td>...</td></tr><tr><td>GW200129_065458</td><td>...</td><td>...</td><td>14.6</td><td>21.2</td><td>6.3</td><td>...</td><td>...</td><td>...</td><td>14.7</td><td>...</td><td>7.1</td><td>14.6</td><td>...</td><td>7.0</td></tr><tr><td>GW200201_203549</td><td>...</td><td>...</td><td>6.2</td><td>5.9</td><td>2.9</td><td>6.1</td><td>5.7</td><td>3.0</td><td>6.1</td><td>5.5</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200202_154313</td><td>...</td><td>...</td><td>4.6</td><td>10.0</td><td>2.4</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>4.8</td><td>9.6</td><td>...</td></tr><tr><td>GW200208_130117</td><td>...</td><td>...</td><td>6.5</td><td>7.4</td><td>4.1</td><td>6.8</td><td>6.6</td><td>4.3</td><td>6.6</td><td>7.0</td><td>...</td><td>6.6</td><td>7.3</td><td>4.5</td></tr><tr><td>GW200208_222617</td><td>...</td><td>...</td><td>5.6</td><td>5.7</td><td>2.1</td><td>5.8</td><td>6.0</td><td>3.2</td><td>...</td><td>...</td><td>...</td><td>5.7</td><td>5.4</td><td>...</td></tr><tr><td>GW200209_085452</td><td>...</td><td>...</td><td>7.5</td><td>6.0</td><td>2.8</td><td>7.1</td><td>6.2</td><td>2.4</td><td>7.0</td><td>6.1</td><td>...</td><td>7.0</td><td>6.1</td><td>...</td></tr><tr><td>GW200210_092254</td><td>...</td><td>...</td><td>4.3</td><td>8.0</td><td>2.9</td><td>...</td><td>...</td><td>...</td><td>4.9</td><td>7.5</td><td>...</td><td>4.9</td><td>7.5</td><td>...</td></tr><tr><td>200214_224526</td><td>7.1</td><td>11.0</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200216_220804</td><td>...</td><td>...</td><td>6.9</td><td>5.9</td><td>2.4</td><td>6.4</td><td>5.7</td><td>2.2</td><td>7.1</td><td>5.6</td><td>...</td><td>6.3</td><td>6.0</td><td>...</td></tr><tr><td>GW200219_094415</td><td>5.8</td><td>7.7</td><td>5.8</td><td>8.7</td><td>2.5</td><td>5.3</td><td>8.8</td><td>2.6</td><td>5.8</td><td>8.0</td><td>...</td><td>5.8</td><td>8.1</td><td>...</td></tr><tr><td>200219_201407</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>12.2</td><td>5.1</td><td>3.3</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200220_061928</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>4.4</td><td>6.0</td><td>...</td></tr><tr><td>GW200220_124850</td><td>...</td><td>...</td><td>6.1</td><td>5.5</td><td>...</td><td>6.1</td><td>5.5</td><td>...</td><td>...</td><td>...</td><td>...</td><td>5.8</td><td>5.2</td><td>...</td></tr><tr><td>GW200224_222234</td><td>13.3</td><td>13.4</td><td>12.5</td><td>12.9</td><td>5.8</td><td>12.6</td><td>13.0</td><td>5.5</td><td>12.7</td><td>12.9</td><td>6.4</td><td>12.2</td><td>12.5</td><td>6.3</td></tr><tr><td>GW200225_060421</td><td>9.6</td><td>8.9</td><td>9.9</td><td>8.2</td><td>...</td><td>9.8</td><td>7.8</td><td>...</td><td>9.4</td><td>7.9</td><td>...</td><td>9.4</td><td>7.9</td><td>...</td></tr><tr><td>GW200302_015811</td><td>...</td><td>...</td><td>10.4</td><td>...</td><td>1.9</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>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>5.9</td><td>6.1</td><td>...</td><td>5.7</td><td>5.4</td><td>...</td><td>5.5</td><td>5.8</td><td>...</td></tr><tr><td>GW200308_173609</td><td>...</td><td>...</td><td>4.9</td><td>6.1</td><td>2.1</td><td>5.1</td><td>5.7</td><td>3.2</td><td>5.1</td><td>6.1</td><td>...</td><td>5.1</td><td>6.1</td><td>...</td></tr><tr><td>GW200311_103121</td><td>...</td><td>...</td><td>5.4</td><td>7.2</td><td>...</td><td>5.7</td><td>7.0</td><td>...</td><td>5.7</td><td>7.2</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200311_115853</td><td>12.0</td><td>11.0</td><td>12.1</td><td>10.7</td><td>7.0</td><td>10.7</td><td>10.4</td><td>6.9</td><td>11.9</td><td>10.2</td><td>6.7</td><td>11.9</td><td>10.7</td><td>6.9</td></tr><tr><td>GW200316_215756</td><td>...</td><td>...</td><td>5.4</td><td>7.9</td><td>3.1</td><td>5.1</td><td>7.2</td><td>3.5</td><td>5.6</td><td>7.4</td><td>...</td><td>5.5</td><td>7.5</td><td>...</td></tr><tr><td>GW200322_091133</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>6.0</td><td>5.8</td><td>3.5</td><td>5.8</td><td>5.6</td><td>...</td><td>5.5</td><td>5.4</td><td>...</td></tr></tbody></table>
<table><caption>TABLE XII. Parameter distributions used to generate injections and to compute the probability of astrophysical origin $p_{astro}$ for each pipeline. The BNS injections are generated using the SpinTaylorT4 waveform model [631,632,634,636–640], while the BBH and NSBH injections are generated using the SEOBNRv4PHM model [137], or the SEOBNRv4P model [137,625,663] for injections corresponding to binaries with redshifted total mass below $9M_{\odot}$. We always use the convention that $m_1 \ge m_2$; this constraint means that the marginalized one-dimensional distributions for the masses will not match the distributions used to define the two-dimensional distributions (as given here) in cases where the $m_1$ and $m_2$ distributions overlap. Masses are in the source frame, except for the PyCBC rows, where the measured (redshifted) chirp mass is considered. The redshift-evolution parameter $\kappa$ controls the injected distribution as described in Eq. (D1). The injection sets are used to estimate sensitive hypervolumes, with weights to match the populations assumed within each $\langle VT \rangle$ calculation, including updating the mass, spin, and redshift distributions where appropriate.</caption><thead><tr><th></th><th></th><th>Mass distribution</th><th>Mass range (M<sub>☉</sub>)</th><th>Spin range</th><th>Spin orientations</th><th>Redshift evolution</th><th>Maximum redshift</th></tr></thead><tbody><tr><td rowspan="6">Injections</td><td rowspan="3">BBH</td><td>$p(m_1) \propto m_1^{-2.35}$</td><td>2 &lt; m<sub>1</sub> &lt; 100</td><td rowspan="3">$|\chi_{1,2}| &lt; 0.998$<br/>$|\chi_1| &lt; 0.998$</td><td rowspan="3">Isotropic</td><td rowspan="3">$\kappa = 1$</td><td rowspan="3">1.9</td></tr><tr><td>$p(m_2|m_1) \propto m_2$</td><td>2 &lt; m<sub>2</sub> &lt; 100</td></tr><tr><td>$p(m_1) \propto m_1^{-2.35}$</td><td>2.5 &lt; m<sub>1</sub> &lt; 60</td></tr><tr><td rowspan="2">NSBH</td><td rowspan="2">Uniform</td><td>1 &lt; m<sub>2</sub> &lt; 2.5</td><td rowspan="2">$|\chi_2| &lt; 0.4$</td><td rowspan="2">Isotropic</td><td rowspan="2">$\kappa = 0$</td><td rowspan="2">0.25</td></tr><tr><td>1 &lt; m<sub>1</sub> &lt; 2.5</td></tr><tr><td>BNS</td><td>Uniform</td><td>1 &lt; m<sub>2</sub> &lt; 2.5</td><td>$|\chi_{1,2}| &lt; 0.4$</td><td>Isotropic</td><td>$\kappa = 0$</td><td>0.15</td></tr><tr><td rowspan="2">cWB p<sub>astro</sub></td><td rowspan="2">BBH</td><td rowspan="2">Same as injections</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3 &lt; m<sub>1</sub> &lt; 300</td><td rowspan="3">$|\chi_{1,2}| &lt; 0.99$<br/>$|\chi_1| &lt; 0.99$</td><td rowspan="3">Aligned</td><td rowspan="3">$\kappa = 0$</td><td rowspan="3">3.76</td></tr><tr><td rowspan="2">BBH</td><td rowspan="2">Log-uniform</td><td>3 &lt; m<sub>2</sub> &lt; 300</td></tr><tr><td>3 &lt; m<sub>1</sub> &lt; 300</td></tr><tr><td rowspan="2">GstLAL p<sub>astro</sub></td><td rowspan="2">NSBH</td><td rowspan="2">Log-uniform</td><td>1 &lt; m<sub>2</sub> &lt; 3</td><td rowspan="2">$|\chi_2| &lt; 0.4$</td><td rowspan="2">Aligned</td><td rowspan="2">$\kappa = 0$</td><td rowspan="2">0.80</td></tr><tr><td>1 &lt; m<sub>1</sub> &lt; 3</td></tr><tr><td>BNS</td><td>Log-uniform</td><td>1 &lt; m<sub>2</sub> &lt; 3</td><td>$|\chi_{1,2}| &lt; 0.05$</td><td>Aligned</td><td>$\kappa = 0$</td><td>0.16</td></tr><tr><td rowspan="5">MBTA p<sub>astro</sub></td><td rowspan="2">BBH</td><td>POWER LAW+PEAK [116]<br/>with $\alpha = 2.5$, $\beta_q = 1.5$, $m_{min} = 5M_{\odot}$, $m_{max} = 80M_{\odot}$,<br/>$\lambda_{peak} = 0.1$, $\mu_m = 34M_{\odot}$,<br/>$\sigma_m = 5M_{\odot}$, $\delta_m = 3.5M_{\odot}$</td><td>5 &lt; m<sub>1</sub> &lt; 80</td><td rowspan="5">$|\chi_{1,2}| &lt; 0.998$</td><td rowspan="5">Isotropic</td><td rowspan="5">$\kappa = 0$</td><td rowspan="5">1.9</td></tr><tr><td>NSBH</td><td>Same as injections</td></tr><tr><td>BNS</td><td>Same as injections</td></tr><tr><td>BBH</td><td>$M > 4.353$</td></tr><tr><td>NSBH</td><td>2.176 &lt; M &lt; 4.353</td></tr><tr><td rowspan="2">PyCBC-broad p<sub>astro</sub></td><td>BNS</td><td>Same as injections</td><td>$M < 2.176$</td><td></td><td></td><td></td><td></td></tr><tr><td>BBH</td><td>$M > 4.353$</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

reweighted to obtain estimates of the sensitive hypervolumes presented in Table III such that the injected distributions in Table XII do not represent the assumed populations used to estimate search sensitivity.

The probability of astrophysical origin $p_{astro}$ for a candidate is estimated directly from the ranking statistics $x$ that are used to assess the FAR. By comparing the distributions of ranking statistics under the assumptions of foreground $p(x|signal)$ or background $p(x|noise)$, we can calculate a signal-versus-noise Bayes factor for each event. This Bayes factor acts as a likelihood in the $p_{astro}$ computation for each event. The normalization of the astrophysical $x$ distributions depends on merger rates, which are jointly estimated in the calculation, assuming that the triggers are drawn from independent Poisson processes [112]. For a given FAR, $p_{astro}$ will be larger if the true alarm rate is higher.

The construction of the foreground (signal) and background (noise) distributions is specific to individual detection pipelines:

(i) The PyCBC analyses use time-shifted triggers to empirically estimate the rates of background events and their distributions over the search ranking statistic, while foreground distributions are estimated using recovered simulated signals. As in GWTC-2.1 [4], we allow these background and foreground distributions to differ between different combinations of detectors in coincidence, and also allow for a dependence of the foreground distribution and signal rate on which detectors are observing at a given time [664]. In order to model variation of the signal rate over binary masses, the foreground and background estimates are obtained separately over the ranges of template chirp mass given in
Table XII; the rate of astrophysical signals is also estimated separately in each range.

(ii) For $G_{\text{stLAL}}$, the ratio of the foreground-to-background distributions (the signal-to-noise Bayes factor that enters into the $p_{\text{astro}}$ calculation) is proportional to the likelihood ratio which is the ranking statistic $x$. Details of the $G_{\text{stLAL}}$ background collection method are given in Appendix D 1. The time-volume sensitivity of the pipeline used in this calculation is estimated based on simulated sources injected into the pipeline and is rescaled to the astrophysical distribution [665]. We use time-volume ratios to combine triggers from various observation runs and perform the multicomponent analysis yielding $p_{\text{astro}}$ and merger rates [112,115] inferred from the entire set of available data (from O1 to O3b).

(iii) The MBTA analysis uses a template bank split into 165 bins in the chirp-mass–mass-ratio parameter space to compute $p_{\text{astro}}$ values of events [117]. The fine binning has the main benefit of allowing the proper tracking over the parameter space of the assumed CBCs populations used in the foreground distribution. It also provides a more tailored estimate of the background rate compared to the FAR reported by the analysis, which uses a coarse estimate of the background (integrated over one of the three search regions) that is conservative for signals from high-mass sources. It can therefore result in events being assigned a significant $p_{\text{astro}}$ in population-rich regions of the parameter space even though they were assigned a high FAR value (examples are GW200220_124850, GW200306_093714, and GW200322_091133). For instance, GW200220_124850 is in an $M-q$ bin that captures 11% of the expected astrophysical signal while it contains only 0.008% of the BBH templates. For the combined ranking statistics of this candidate, the expected foreground rate density (per unit interval of the ranking statistic squared) is $0.109 \text{ yr}^{-1}$, while the local background rate density is $0.023 \text{ yr}^{-1}$. For each of the bins, the background is constructed by making random coincidences of single-detector triggers for each coincidence type (HL, LV, HV, or HLV) using the templates of the bin considered, but only during HL and HLV coincidence time to remove single-detector events from the background estimation [82,83]. This means that the background assigned to an event depends on its coincidence type and on the bin which triggered the associated template. The foreground for the BNS and NSBH categories is estimated using the populations described in Table XII. The foreground estimate for the BBH uses the POWER LAW+PEAK population model used to describe the GWTC-2 population [116,666].

(iv) Just as PyCBC, cWB also uses time-shifted analysis for significance assessment of background and foreground triggers. The distribution of the coherent network SNR ranking statistic for the time-shifted triggers is used to estimate the background, and consequently to assign the FAR. The foreground is derived from the recovered simulated signals. Since cWB is significantly more sensitive to BBH systems, only these sources are considered.

The precise $p_{\text{astro}}$ value depends upon the assumed true population, and hence may be subject to change as we learn more about the astrophysical population of CBCs. The population models used by the various pipelines in their computation of $p_{\text{astro}}$ are summarized in Table XII.

When estimating $p_{\text{astro}}$ for each candidate, we do so separately for each category of source, as $p_{\text{astro}}$ is dependent on the underlying BNS, NSBH, and BBH populations. We separate the candidates based on their component masses; rather than a rigorous statement of the nature of the component, the NS label is used only to identify components whose masses are below $3M_{\odot}$. BBH-category candidates are any for which component masses are both above $3M_{\odot}$, BNS-category candidates are the ones for which both component masses fall below this value, and we consider a candidate a part of the NSBH category if the primary component mass was above this boundary, and the secondary below it. The category chosen for each source is based on the masses of the template found by the search pipeline, rather than a detailed inference of source properties (Sec. V); this may lead to $p_{\text{astro}}$ estimates that are biased relative to an ideal calculation using the full information available for the signals.

In Table XIII, we give the calculated probabilities that a candidate comes from a system in our BBH category $p_{\text{BBH}}$, our NSBH category $p_{\text{NSBH}}$, or our BNS category $p_{\text{BNS}}$. The probability that a candidate belongs to a specific astrophysical source category ($p_{\text{BNS}}$, $p_{\text{NSBH}}$, or $p_{\text{BBH}}$) is evaluated from source-class-specific Bayes factors by redistributing the foreground probabilities across astrophysical source classes. This redistribution makes use of the template-based estimate of the component masses of the candidate, as well as the response of the template bank to an assumed population of BNS, NSBH and BBH signals. The computation of the probability that a candidate comes from a system in one of the three astrophysical categories requires the choice of a prior on the counts in each category [114]. $G_{\text{stLAL}}$ used a uniform prior for the BNS and NSBH categories and a Poisson-Jeffreys prior for the BBH category, MBTA used a uniform prior for the BNS category and a Poisson-Jeffreys prior for the NSBH and BBH categories, PyCBC used a Poisson-Jeffreys prior for all three categories, and cWB used a Poisson-Jeffreys prior. Given the number of candidates, the prior choice does not significantly impact the BBH results, but can influence the BNS and NSBH $p_{\text{astro}}$ values (e.g., variations of 0.045 for GW200105_162426).
<table><caption>TABLE XIII. Multicomponent $p_{astro}$ values for candidates with $p_{astro} > 0.5$ and marginal candidates with FAR < 2.0 yr$^{-1}$ where the probability of a BNS or NSBH category is nonzero in any search analysis. Since cWB does not calculate separate source probabilities, all sources are treated as BBHs for the purposes of $p_{astro}$ calculation. Results in italics indicate where an analysis found the candidate with $p_{astro} < 0.5$, and three center dots (· · ·) indicate that a candidate was not found by an analysis. Source probability for BNS is not given for PyCBC-BBH, as the search is not sensitive to redshifted chirp masses below $4.353M_{\odot}$. This would require extremely high redshifts, to which LIGO and Virgo are not sensitive, to correspond to a BNS source. The BNS, NSBH, and BBH categories are defined by the masses associated with the candidate from the search results (as defined in Table XII), and do not necessarily correspond to the true astrophysical population of sources.</caption><thead><tr><th rowspan="2">Name</th><th colspan="1">cWB</th><th colspan="4">GstLAL</th><th colspan="4">MBTA</th><th colspan="4">PyCBC-broad</th><th colspan="4">PyCBC-BBH</th></tr><tr><th>P<sub>astro</sub></th><th>P<sub>BBH</sub></th><th>P<sub>NSBH</sub></th><th>P<sub>BNS</sub></th><th>P<sub>astro</sub></th><th>P<sub>BBH</sub></th><th>P<sub>NSBH</sub></th><th>P<sub>BNS</sub></th><th>P<sub>astro</sub></th><th>P<sub>BBH</sub></th><th>P<sub>NSBH</sub></th><th>P<sub>BNS</sub></th><th>P<sub>astro</sub></th><th>P<sub>BBH</sub></th><th>P<sub>NSBH</sub></th><th>P<sub>astro</sub></th></tr></thead><tbody><tr><td>GW191118_212859</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.04</td><td>&lt;0.01</td><td>0.05</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200105_162426</td><td>...</td><td>&lt;0.01</td><td>0.36</td><td>&lt;0.01</td><td>0.36</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>200121_031748</td><td>...</td><td>0.02</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.02</td><td>0.22</td><td>0.01</td><td>&lt;0.01</td><td>0.23</td><td>...</td><td>...</td><td>...</td><td>...</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td></tr><tr><td>GW200201_203549</td><td>...</td><td>&lt;0.01</td><td>0.12</td><td>&lt;0.01</td><td>0.12</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>...</td><td>...</td><td>...</td></tr><tr><td>200219_201407</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.45</td><td>0.03</td><td>&lt;0.01</td><td>0.48</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200311_103121</td><td>...</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.03</td><td>0.03</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.19</td><td>0.19</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW191103_012549</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.13</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.13</td><td>0.67</td><td>0.10</td><td>&lt;0.01</td><td>0.77</td><td>0.81</td><td>0.14</td><td>0.94</td></tr><tr><td>GW191105_143521</td><td>...</td><td>0.07</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.07</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.81</td><td>0.19</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.81</td><td>0.19</td><td>&gt;0.99</td></tr><tr><td>GW191126_115259</td><td>...</td><td>0.02</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.02</td><td>0.30</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.30</td><td>0.38</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.39</td><td>0.69</td><td>0.01</td><td>0.70</td></tr><tr><td>GW191127_050227</td><td>...</td><td>0.34</td><td>0.14</td><td>&lt;0.01</td><td>0.49</td><td>0.73</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.73</td><td>0.47</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.47</td><td>0.74</td><td>&lt;0.01</td><td>0.74</td></tr><tr><td>GW191129_134029</td><td>...</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.72</td><td>0.28</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.72</td><td>0.28</td><td>&gt;0.99</td></tr><tr><td>GW191204_171526</td><td>&gt;0.99</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.98</td><td>0.02</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.98</td><td>0.02</td><td>&gt;0.99</td></tr><tr><td>GW191216_213338</td><td>...</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.91</td><td>0.09</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.91</td><td>0.09</td><td>&gt;0.99</td></tr><tr><td>GW191219_163120</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.20</td><td>0.63</td><td>&lt;0.01</td><td>0.82</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW191222_033537</td><td>&gt;0.99</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&gt;0.99</td></tr><tr><td>GW200115_042309</td><td>...</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&gt;0.99</td><td>&lt;0.01</td><td>0.93</td><td>0.07</td><td>&gt;0.99</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW200202_154313</td><td>...</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.67</td><td>0.33</td><td>&gt;0.99</td></tr><tr><td>GW200210_092254</td><td>...</td><td>0.40</td><td>0.03</td><td>&lt;0.01</td><td>0.42</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.31</td><td>0.22</td><td>&lt;0.01</td><td>0.53</td><td>0.31</td><td>0.23</td><td>0.54</td></tr><tr><td>GW200316_215756</td><td>...</td><td>&gt;0.99</td><td>&lt;0.01</td><td>&lt;0.01</td><td>&gt;0.99</td><td>0.30</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.30</td><td>0.98</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.98</td><td>0.95</td><td>0.03</td><td>0.98</td></tr></tbody></table>

In addition to the choice of prior on count, $p_{BNS}$, $p_{NSBH}$, and $p_{BBH}$ also depend upon the assumed foreground and background. The methods to redistribute the foreground probabilities across astrophysical source classes are specific to individual detection pipelines:

(i) **GstLAL** classifies signals into BNS, NSBH, and BBH using a semianalytic template weighting scheme [667], which is needed for a multicomponent $p_{astro}$ calculation [115]. The response of each template to signals from the different categories is computed assuming Gaussian noise [667] instead of using simulated signals. For a given trigger, the template identified for this classification is the one which has the highest SNR divided by the value of the signal-based-veto test, rather than the one with the highest likelihood ratio.

(ii) For MBTA, the fraction of recovered simulated signals from each category is used to infer the probabilities [117]. Following GWTC-2.1 [4], this analysis assumes an astrophysical population where BNSs have a maximum component mass of $2.5M_{\odot}$, NSBHs have one component above $2.5M_{\odot}$ and one

below $2.5M_{\odot}$, and BBHs have both components above $5M_{\odot}$. While this division between NSs and BHs does not match the other analyses, it should preserve our goal of the BBH category only including confident BHs with masses above $3M_{\odot}$, while the BNS and NSBH categories include any systems that could contain a NS (as well as potentially some low-mass BHs).

(iii) For PyCBC, categories are assigned based on the source chirp mass. This is estimated by correcting the redshifted template masses using a luminosity distance derived from the SNRs [613]. As the PyCBC-BBH analysis is not sensitive to redshifted chirp masses below $4.353M_{\odot}$ (corresponding to an equal-mass binary with components of $5M_{\odot}$), we do not calculate $p_{BNS}$ for this analysis.

(iv) As discussed above, cWB is most sensitive to BBH signals, and, in this analysis, BBHs are the only astrophysical source class considered for this pipeline. The assumption that all signals identified by cWB correspond to CBCs is discussed further in Appendix F.
Given our current uncertainties on the maximum NS mass and minimum BH mass, the three categories do not necessarily reflect the true nature of the source, but should serve to highlight candidates of interest if looking for potential BNSs or NSBHs, or a clean sample of BBHs.

The precise values of astrophysical source-class probabilities are generally insensitive to assumptions for candidates confidently identified as noise ($p_{astro} \sim 0$) or signal ($p_{astro} \sim 1$). However, marginal $p_{astro}$ estimates ($p_{astro} \sim 0.5$) tend to fluctuate by $O(0.1)$ based on various choices made [117]:

(i) The choice of distribution of masses used to estimate the foreground model. Since the true distribution of BNSs, NSBHs, and BBHs is unknown, the marginal $p_{astro}$ values are subject to this uncertainty.

(ii) The choice of injection distributions used to assess the response of the template banks to different astrophysical source classes. Given our lack of knowledge of the true distribution of intrinsic parameters for BNS, NSBH, and BBH systems, uncertainties germane to this choice are especially pertinent to the MBTA estimations of $p_{astro}$. For GstLAL, the classification is most sensitive to the choice of upper limit on the NS mass distribution, as only triggers falling close to this threshold will have an ambiguous classification. For PyCBC, the corresponding uncertainty comes from the choice of threshold on $M$ used to assign a candidate to the BBH source class. Using the response of the template as a means to account for biases in the

template-based estimate of intrinsic parameters is itself expected to be suboptimal as compared to a full inference of these parameters, and is therefore itself a source of uncertainty.

(iii) The location of the boundary between source classes in mass space. The upper limit on the NS mass is set at $3M_{\odot}$, although the true boundary is unknown. Marginal candidates with components close to this boundary could have significantly different $p_{astro}$ depending on which side of the boundary the template estimates of their masses put them. For example, a marginal candidate categorized as BBH would have a larger $p_{astro}$ than the same candidate categorized as NSBH, since $p_{astro}$ depends on the number of foreground candidates pertaining to these source categories; this is the case of GW191219_163120.

(iv) Specifically for single-detector candidates, the background distribution must be extrapolated to evaluate the background probability. For coincident candidates, the background models are built from random coincidences from data between pairs of detectors time shifted with respect to each other, which is not possible for single-detector candidates.

While the above captures some of the primary factors that affect the values of marginal $p_{astro}$, the list is not exhaustive. Marginal $p_{astro}$ values also depend on other factors which are specific to the analysis methods used by different detection pipelines. Additionally, we expect that the estimated values of $p_{astro}$ may change as we learn more about the various astrophysical populations.

<table><caption>TABLE XIV. Sensitive hypervolume $\langle VT \rangle$ for the various search analyses for all of O3 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 sets of binary masses and distribution of injections found in this bin are the same as given in Table III. As in Table III, where insufficient numbers of injections are recovered such that the sensitive hypervolume cannot be accurately estimated; these cases are indicated by three center dots (·).</caption><thead><tr><th colspan="3">Binary masses (M<sub>☉</sub>)</th><th colspan="7">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>5.5<sup>+0.1</sup><sub>-0.2</sub></td><td>8.8<sup>+0.2</sup><sub>-0.2</sub></td><td>7.4<sup>+0.2</sup><sub>-0.2</sub></td><td>6.9<sup>+0.1</sup><sub>-0.2</sub></td><td>9.2<sup>+0.2</sup><sub>-0.2</sub></td><td>11.2<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>35.0</td><td>20.0</td><td>22.9</td><td>2.7<sup>+0.1</sup><sub>-0.2</sub></td><td>4.9<sup>+0.2</sup><sub>-0.2</sub></td><td>3.9<sup>+0.2</sup><sub>-0.1</sub></td><td>3.9<sup>+0.2</sup><sub>-0.1</sub></td><td>5.3<sup>+0.2</sup><sub>-0.2</sub></td><td>6.4<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>35.0</td><td>1.5</td><td>5.2</td><td>...</td><td>3.8<sup>+0.3</sup><sub>-0.4</sub> × 10<sup>-2</sup></td><td>3.7<sup>+0.4</sup><sub>-0.4</sub> × 10<sup>-2</sup></td><td>6.2<sup>+0.4</sup><sub>-0.5</sub> × 10<sup>-2</sup></td><td>...</td><td>6.6<sup>+0.5</sup><sub>-0.5</sub> × 10<sup>-2</sup></td></tr><tr><td>20.0</td><td>20.0</td><td>17.4</td><td>1.19<sup>+0.05</sup><sub>-0.05</sub></td><td>2.82<sup>+0.08</sup><sub>-0.08</sub></td><td>2.41<sup>+0.07</sup><sub>-0.08</sub></td><td>2.38<sup>+0.07</sup><sub>-0.08</sub></td><td>2.99<sup>+0.09</sup><sub>-0.08</sub></td><td>3.57<sup>+0.09</sup><sub>-0.09</sub></td></tr><tr><td>20.0</td><td>10.0</td><td>12.2</td><td>0.48<sup>+0.05</sup><sub>-0.05</sub></td><td>1.25<sup>+0.07</sup><sub>-0.07</sub></td><td>1.10<sup>+0.06</sup><sub>-0.07</sub></td><td>1.14<sup>+0.07</sup><sub>-0.07</sub></td><td>1.32<sup>+0.07</sup><sub>-0.08</sub></td><td>1.56<sup>+0.08</sup><sub>-0.08</sub></td></tr><tr><td>20.0</td><td>1.5</td><td>4.2</td><td>...</td><td>3.9<sup>+0.2</sup><sub>-0.3</sub> × 10<sup>-2</sup></td><td>3.4<sup>+0.3</sup><sub>-0.2</sub> × 10<sup>-2</sup></td><td>5.4<sup>+0.3</sup><sub>-0.3</sub> × 10<sup>-2</sup></td><td>...</td><td>6.0<sup>+0.3</sup><sub>-0.4</sub> × 10<sup>-2</sup></td></tr><tr><td>10.0</td><td>10.0</td><td>8.7</td><td>0.15<sup>+0.01</sup><sub>-0.01</sub></td><td>0.59<sup>+0.02</sup><sub>-0.03</sub></td><td>0.53<sup>+0.02</sup><sub>-0.02</sub></td><td>0.56<sup>+0.03</sup><sub>-0.02</sub></td><td>0.59<sup>+0.03</sup><sub>-0.02</sub></td><td>0.72<sup>+0.02</sup><sub>-0.03</sub></td></tr><tr><td>10.0</td><td>5.0</td><td>6.1</td><td>3.6<sup>+0.9</sup><sub>-0.8</sub> × 10<sup>-2</sup></td><td>0.25<sup>+0.02</sup><sub>-0.03</sub></td><td>0.23<sup>+0.02</sup><sub>-0.02</sub></td><td>0.27<sup>+0.02</sup><sub>-0.03</sub></td><td>0.26<sup>+0.02</sup><sub>-0.02</sub></td><td>0.31<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>10.0</td><td>1.5</td><td>3.1</td><td>...</td><td>3.5<sup>+0.1</sup><sub>-0.2</sub> × 10<sup>-2</sup></td><td>3.3<sup>+0.2</sup><sub>-0.1</sub> × 10<sup>-2</sup></td><td>3.8<sup>+0.1</sup><sub>-0.2</sub> × 10<sup>-2</sup></td><td>...</td><td>4.5<sup>+0.1</sup><sub>-0.2</sub> × 10<sup>-2</sup></td></tr><tr><td>5.0</td><td>5.0</td><td>4.4</td><td>1.1<sup>+0.2</sup><sub>-0.2</sub> × 10<sup>-2</sup></td><td>0.129<sup>+0.007</sup><sub>-0.006</sub></td><td>9.8<sup>+0.6</sup><sub>-0.6</sub> × 10<sup>-2</sup></td><td>0.138<sup>+0.007</sup><sub>-0.007</sub></td><td>0.108<sup>+0.006</sup><sub>-0.006</sub></td><td>0.158<sup>+0.008</sup><sub>-0.007</sub></td></tr><tr><td>5.0</td><td>1.5</td><td>2.3</td><td>...</td><td>2.34<sup>+0.08</sup><sub>-0.08</sub> × 10<sup>-2</sup></td><td>2.41<sup>+0.08</sup><sub>-0.08</sub> × 10<sup>-2</sup></td><td>2.47<sup>+0.08</sup><sub>-0.08</sub> × 10<sup>-2</sup></td><td>...</td><td>2.96<sup>+0.09</sup><sub>-0.09</sub> × 10<sup>-2</sup></td></tr><tr><td>1.5</td><td>1.5</td><td>1.3</td><td>...</td><td>5.8<sup>+0.2</sup><sub>-0.1</sub> × 10<sup>-3</sup></td><td>7.0<sup>+0.2</sup><sub>-0.2</sub> × 10<sup>-3</sup></td><td>7.3<sup>+0.2</sup><sub>-0.2</sub> × 10<sup>-3</sup></td><td>...</td><td>8.2<sup>+0.2</sup><sub>-0.2</sub> × 10<sup>-3</sup></td></tr></tbody></table>
Using the expanded list of candidates including the subthreshold candidates, it is possible to use updated population models to reevaluate $p_{astro}$ and compile revised lists of probable GW candidates.

### a. Results for all of O3

Here we present results from all of O3, giving sensitivity estimates for the points in parameter space discussed in Sec. IV E 1 from injections covering all of O3, and the updated $p_{astro}$ for candidates in O3a given the updated event-rate information inclusive of O3b.

The sensitive hypervolume $\langle VT \rangle$ for each search analysis for all of O3 is presented in Table XIV. These results show the same trends as shown in Table III and Fig. 6 for O3b.

However, the values are naturally larger on account of the greater observing time.

Finally, in Table XV we provide updated calculations of $p_{astro}$ for O3a candidates which were published in GWTC-2.1 [4] with $p_{astro} > 0.5$ using data from all of O3. For the first time for these candidates, we also report $p_{astro}$ as calculated by the cWB pipeline. While there are small changes in value compared to the calculation using only O3a data, there are no changes in the list of candidates with $p_{astro} > 0.5$. The change in $p_{astro}$ for GW190425, from 0.78 in GWTC-2.1 to 0.69 here, stems from the increased $\langle VT \rangle$ with no new confirmed BNS detection in O3b, and illustrates how medium-range $p_{astro}$ values are subject to vary with our knowledge of source populations.

<table><caption>TABLE XV. Updated probability of astrophysical origin $p_{astro}$, FAR, and SNR values for candidates from O3a using data from the whole of O3. We include $p_{astro}$ values for any candidates that were published in GWTC-2.1 [4] with $p_{astro} > 0.5$. Using all of the O3 data, there are no changes to the list of candidates with $p_{astro} > 0.5$. As in Table I, results in italics indicate where an analysis found the candidate with $p_{astro} < 0.5$, and three center dots (· · ·) indicate that a candidate was not found by an analysis. Although cWB contributed to the analysis of GW190814 [241], it is not included in the cWB column because it was not detected with LV alone with the standard data-quality vetoes, but required a manual override of the LIGO Hanford vetoes. This table updates Table I of GWTC-2.1 [4].</caption><thead><tr><th rowspan="2">Name</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>GW190403_051519</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>7.7</td><td>8.0</td><td>0.60</td></tr><tr><td>GW190408_181802</td><td>9.5 &times; 10<sup>-4</sup></td><td>14.8</td><td>&gt;0.99</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>15</td><td>&gt;0.99</td><td>8.7 &times; 10<sup>-5</sup></td><td>14</td><td>&gt;0.99</td><td>2.5 &times; 10<sup>-4</sup></td><td>13</td><td>&gt;0.99</td><td>&lt;1.2 &times; 10<sup>-4</sup></td><td>14</td><td>&gt;0.99</td></tr><tr><td>GW190412</td><td>9.5 &times; 10<sup>-4</sup></td><td>19.7</td><td>&gt;0.99</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>19</td><td>&gt;0.99</td><td>1.0 &times; 10<sup>-5</sup></td><td>18</td><td>&gt;0.99</td><td>&lt;1.1 &times; 10<sup>-4</sup></td><td>17</td><td>&gt;0.99</td><td>&lt;1.2 &times; 10<sup>-4</sup></td><td>18</td><td>&gt;0.99</td></tr><tr><td>GW190413_052954</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>170</td><td>8.5</td><td>0.12</td><td>0.82</td><td>8.5</td><td>0.92</td></tr><tr><td>GW190413_134308</td><td>...</td><td>...</td><td>...</td><td>39</td><td>10</td><td>0.03</td><td>0.34</td><td>10</td><td>0.99</td><td>21</td><td>9.3</td><td>0.47</td><td>0.18</td><td>8.9</td><td>0.99</td></tr><tr><td>GW190421_213856</td><td>0.30</td><td>9.3</td><td>0.90</td><td>0.0028</td><td>10</td><td>&gt;0.99</td><td>1.2</td><td>9.7</td><td>0.99</td><td>5.9</td><td>10</td><td>0.74</td><td>0.014</td><td>10</td><td>&gt;0.99</td></tr><tr><td>GW190425</td><td>...</td><td>...</td><td>...</td><td>0.034</td><td>13</td><td>0.69</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW190426_190642</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>4.1</td><td>9.6</td><td>0.73</td></tr><tr><td>GW190503_185404</td><td>0.0018</td><td>11.5</td><td>&gt;0.99</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td><td>0.013</td><td>13</td><td>&gt;0.99</td><td>0.038</td><td>12</td><td>&gt;0.99</td><td>0.0026</td><td>12</td><td>&gt;0.99</td></tr><tr><td>GW190512_180714</td><td>0.88</td><td>10.7</td><td>0.75</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td><td>0.038</td><td>12</td><td>0.98</td><td>1.1 &times; 10<sup>-4</sup></td><td>12</td><td>&gt;0.99</td><td>&lt;1.1 &times; 10<sup>-4</sup></td><td>12</td><td>&gt;0.99</td></tr><tr><td>GW190513_205428</td><td>...</td><td>...</td><td>...</td><td>1.3 &times; 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td><td>0.11</td><td>13</td><td>0.99</td><td>19</td><td>12</td><td>0.48</td><td>0.044</td><td>12</td><td>&gt;0.99</td></tr><tr><td>GW190514_065416</td><td>...</td><td>...</td><td>...</td><td>450</td><td>8.3</td><td>&lt;0.01</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>2.8</td><td>8.4</td><td>0.75</td></tr><tr><td>GW190517_055101</td><td>0.0065</td><td>10.7</td><td>&gt;0.99</td><td>0.0045</td><td>11</td><td>&gt;0.99</td><td>0.11</td><td>11</td><td>&gt;0.99</td><td>0.0095</td><td>10</td><td>&gt;0.99</td><td>3.5 &times; 10<sup>-4</sup></td><td>10</td><td>&gt;0.99</td></tr><tr><td>GW190519_153544</td><td>3.1 &times; 10<sup>-4</sup></td><td>14.0</td><td>&gt;0.99</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td><td>7.0 &times; 10<sup>-5</sup></td><td>14</td><td>&gt;0.99</td><td>&lt;1.0 &times; 10<sup>-4</sup></td><td>13</td><td>&gt;0.99</td><td>&lt;1.1 &times; 10<sup>-4</sup></td><td>13</td><td>&gt;0.99</td></tr><tr><td>GW190521</td><td>2.0 &times; 10<sup>-4</sup></td><td>14.4</td><td>&gt;0.99</td><td>0.20</td><td>13</td><td>0.77</td><td>0.042</td><td>13</td><td>0.96</td><td>0.44</td><td>14</td><td>0.96</td><td>0.0013</td><td>14</td><td>&gt;0.99</td></tr><tr><td>GW190521_074359</td><td>1.0 &times; 10<sup>-4</sup></td><td>24.7</td><td>&gt;0.99</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>24</td><td>&gt;0.99</td><td>1.0 &times; 10<sup>-5</sup></td><td>22</td><td>&gt;0.99</td><td>&lt;1.8 &times; 10<sup>-5</sup></td><td>24</td><td>&gt;0.99</td><td>&lt;2.3 &times; 10<sup>-5</sup></td><td>24</td><td>&gt;0.99</td></tr><tr><td>GW190527_092055</td><td>...</td><td>...</td><td>...</td><td>0.23</td><td>8.7</td><td>0.83</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>19</td><td>8.4</td><td>0.31</td></tr><tr><td>GW190602_175927</td><td>0.015</td><td>11.1</td><td>&gt;0.99</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td><td>3.0 &times; 10<sup>-4</sup></td><td>13</td><td>&gt;0.99</td><td>0.29</td><td>12</td><td>0.98</td><td>0.013</td><td>12</td><td>&gt;0.99</td></tr><tr><td>GW190620_030421</td><td>...</td><td>...</td><td>...</td><td>0.011</td><td>11</td><td>0.99</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW190630_185205</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>15</td><td>&gt;0.99</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.24</td><td>15</td><td>&gt;0.99</td></tr><tr><td>GW190701_203306</td><td>0.32</td><td>10.2</td><td>0.89</td><td>0.0057</td><td>12</td><td>&gt;0.99</td><td>35</td><td>11</td><td>0.85</td><td>0.064</td><td>12</td><td>&gt;0.99</td><td>0.56</td><td>12</td><td>&gt;0.99</td></tr><tr><td>GW190706_222641</td><td>0.0010</td><td>12.7</td><td>&gt;0.99</td><td>5.0 &times; 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td><td>0.0015</td><td>12</td><td>&gt;0.99</td><td>3.7 &times; 10<sup>-4</sup></td><td>12</td><td>&gt;0.99</td><td>0.34</td><td>13</td><td>&gt;0.99</td></tr><tr><td>GW190707_093326</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td><td>0.032</td><td>13</td><td>&gt;0.99</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td><td>&lt;1.9 &times; 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td></tr><tr><td>GW190708_232457</td><td>...</td><td>...</td><td>...</td><td>3.1 &times; 10<sup>-4</sup></td><td>13</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>GW190719_215514</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.63</td><td>8.0</td><td>0.91</td></tr><tr><td>GW190720_000836</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 &times; 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td><td>0.094</td><td>12</td><td>&gt;0.99</td><td>1.4 &times; 10<sup>-4</sup></td><td>11</td><td>&gt;0.99</td><td>&lt;7.8 &times; 10<sup>-5</sup></td><td>11</td><td>&gt;0.99</td></tr></tbody></table>

(Table continued)
<table><caption>TABLE XV. (Continued)</caption><thead><tr><th rowspan="2">Name</th><th colspan="3">CWB</th><th colspan="3">GS&LAL</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>GW190725_174728</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>3.1</td><td>9.8</td><td>0.56</td><td>0.46</td><td>9.1</td><td>0.96</td><td>2.9</td><td>8.8</td><td>0.80</td></tr><tr><td>GW190727_060333</td><td>0.088</td><td>11.4</td><td>0.95</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td><td>0.023</td><td>12</td><td>&gt;0.99</td><td>0.0056</td><td>11</td><td>&gt;0.99</td><td>2.0 × 10<sup>-4</sup></td><td>11</td><td>&gt;0.99</td></tr><tr><td>GW190728_064510</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td><td>7.5 × 10<sup>-4</sup></td><td>13</td><td>&gt;0.99</td><td>&lt;8.2 × 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td><td>&lt;7.8 × 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td></tr><tr><td>GW190731_140936</td><td>...</td><td>...</td><td>...</td><td>0.33</td><td>8.5</td><td>0.76</td><td>6.1</td><td>9.1</td><td>0.78</td><td>...</td><td>...</td><td>...</td><td>1.9</td><td>7.8</td><td>0.83</td></tr><tr><td>GW190803_022701</td><td>...</td><td>...</td><td>...</td><td>0.073</td><td>9.1</td><td>0.93</td><td>77</td><td>9.0</td><td>0.95</td><td>81</td><td>8.7</td><td>0.16</td><td>0.39</td><td>8.7</td><td>0.97</td></tr><tr><td>GW190805_211137</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.63</td><td>8.3</td><td>0.95</td></tr><tr><td>GW190814</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>22</td><td>&gt;0.99</td><td>2.0 × 10<sup>-4</sup></td><td>20</td><td>&gt;0.99</td><td>0.17</td><td>19</td><td>&gt;0.99</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW190828_063405</td><td>9.6 × 10<sup>-4</sup></td><td>16.6</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>16</td><td>&gt;0.99</td><td>1.0 × 10<sup>-5</sup></td><td>15</td><td>&gt;0.99</td><td>&lt;8.5 × 10<sup>-5</sup></td><td>14</td><td>&gt;0.99</td><td>&lt;7.0 × 10<sup>-5</sup></td><td>16</td><td>&gt;0.99</td></tr><tr><td>GW190828_065509</td><td>...</td><td>...</td><td>...</td><td>3.5 × 10<sup>-5</sup></td><td>11</td><td>&gt;0.99</td><td>0.16</td><td>11</td><td>0.96</td><td>2.8 × 10<sup>-4</sup></td><td>11</td><td>&gt;0.99</td><td>1.1 × 10<sup>-4</sup></td><td>11</td><td>&gt;0.99</td></tr><tr><td>GW190910_112807</td><td>...</td><td>...</td><td>...</td><td>0.0029</td><td>13</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>GW190915_235702</td><td>0.0010</td><td>12.3</td><td>&gt;0.99</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td><td>0.0055</td><td>13</td><td>&gt;0.99</td><td>6.8 × 10<sup>-4</sup></td><td>13</td><td>&gt;0.99</td><td>&lt;7.0 × 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td></tr><tr><td>GW190916_200658</td><td>...</td><td>...</td><td>...</td><td>12</td><td>8.2</td><td>0.08</td><td>6.9 × 10<sup>3</sup></td><td>8.2</td><td>0.62</td><td>...</td><td>...</td><td>...</td><td>4.7</td><td>7.9</td><td>0.62</td></tr><tr><td>GW190917_114630</td><td>...</td><td>...</td><td>...</td><td>0.66</td><td>9.5</td><td>0.74</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>GW190924_021846</td><td>...</td><td>...</td><td>...</td><td>&lt;1.0 × 10<sup>-5</sup></td><td>13</td><td>&gt;0.99</td><td>0.0049</td><td>12</td><td>&gt;0.99</td><td>&lt;8.2 × 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td><td>8.3 × 10<sup>-5</sup></td><td>12</td><td>&gt;0.99</td></tr><tr><td>GW190925_232845</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>100</td><td>9.4</td><td>0.32</td><td>73</td><td>9.0</td><td>0.03</td><td>0.0072</td><td>9.9</td><td>0.99</td></tr><tr><td>GW190926_050336</td><td>...</td><td>...</td><td>...</td><td>1.1</td><td>9.0</td><td>0.51</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>87</td><td>7.8</td><td>0.09</td></tr><tr><td>GW190929_012149</td><td>...</td><td>...</td><td>...</td><td>0.16</td><td>10</td><td>0.86</td><td>2.9</td><td>10</td><td>0.61</td><td>120</td><td>9.4</td><td>0.14</td><td>14</td><td>8.5</td><td>0.40</td></tr><tr><td>GW190930_133541</td><td>...</td><td>...</td><td>...</td><td>0.43</td><td>10</td><td>0.74</td><td>0.34</td><td>10.0</td><td>0.86</td><td>0.018</td><td>9.8</td><td>&gt;0.99</td><td>0.012</td><td>10</td><td>&gt;0.99</td></tr></tbody></table>

## APPENDIX E: PARAMETER-ESTIMATION METHODS

To determine the astrophysical parameters of each signal's source, we employ statistical inference techniques on the data from the interferometers. We calculate the posterior probability distribution $p(\vec{\theta}|d)$ for the source parameters $\vec{\theta}$ using Bayes's theorem [668],

$$p(\vec{\theta}|d) \propto p(d|\vec{\theta})p(\vec{\theta}), \quad (E1)$$

where the posterior is proportional to the prior probability distributions on the parameters $p(\vec{\theta})$, and the likelihood $p(d|\vec{\theta})$, which is the probability the data $d$ would be observed given a model with parameters $\vec{\theta}$. Our analysis matches that performed for GWTC-2.1 [4].

Results from a number of analysis pipelines are presented in this work, but the principles used to construct the likelihood are the same for each [131]. The data from each interferometer are analyzed coherently, making the assumption that the noise can be treated as stationary, Gaussian, and independent between each of the interferometers used in the analysis over the duration analyzed for each signal [96,669]. These assumptions result in a Gaussian likelihood [135] for a single interferometer,

$$p(d^k|\vec{\theta}) \propto \exp \left[ -\frac{1}{2} \langle d^k - h_M^k | d^k - h_M^k \rangle \right], \quad (E2)$$

where $d^k$ is the data and $h_M^k$ the waveform model evaluated at $\vec{\theta}$ as measured by the interferometer (incorporating the detector response [670,671] and adjusted for detector calibration). The operation $\langle |\cdot| \cdot \rangle$ represents the noise-weighted inner product [382], which requires the precalculation of the PSD of the noise, and a choice of frequency ranges over which the product should be calculated:

(i) The minimum frequency $f_{\text{low}}$ for the inner product is chosen to be 20 Hz.

(ii) The maximum frequency is set as $f_{\text{high}} = \alpha^{\text{roll-off}}(f_s/2)$, where $f_s$ is the sampling frequency ($f_s/2$ is the Nyquist frequency), and $\alpha^{\text{roll-off}}$ is included to avoid power loss due to the application of a window function. We limit power loss to 1%, which for the adopted Butterworth filter [146,376] requires $\alpha^{\text{roll-off}} = 0.875$. To limit computational cost, the sampling rate is typically limited to $f_s = 4096$ Hz or $f_s = 8192$ Hz, and a lower rate is used when $f_{\text{high}}$ is high enough to fully resolve the $(\ell, |m|) = (3, 3)$ multipole moments. Given current detector sensitivity, we do not expect to gain significant information by using sampling rates above $f_s \sim 4096$ Hz.

(iii) The noise PSD for each candidate is estimated using BayesWave [379,672]. The PSD is either estimated using the same data used for the likelihood calculation or for an equivalent length of adjacent data. We use the median inferred PSD value at each frequency [673,674]. The various PSDs are precalculated for each candidate and used in each of the parameter-estimation studies for that candidate.
<table><caption>TABLE XVI. List of data used and mitigation methods applied to data surrounding each candidate prior to source-parameter estimation. We list the candidates for which we perform mitigation of instrumental artifacts; there are seven candidates reported in Table I and the previously reported GW200105_162426 [8]. For all analyses using Virgo data, calibration error at approximately 50 Hz is mitigated by notching out the relevant frequency range. The noise-subtraction methods (BayesWave [377,379] glitch modeling and gwsubtract linear subtraction using a witness [44,59]) used for these candidates are detailed in Appendix C.</caption><thead><tr><td>Candidate</td><td>Affected detectors</td><td>Mitigation</td></tr></thead><tbody><tr><td>GW191105_143521</td><td>Virgo</td><td>BayesWave deglitching</td></tr><tr><td>GW191109_010717</td><td>Hanford, Livingston</td><td>BayesWave deglitching</td></tr><tr><td>GW191113_071753</td><td>Hanford</td><td>BayesWave deglitching</td></tr><tr><td>GW191127_050227</td><td>Hanford</td><td>BayesWave deglitching</td></tr><tr><td>GW191219_163120</td><td>Hanford, Livingston</td><td>BayesWave deglitching</td></tr><tr><td>GW200105_162426</td><td>Livingston</td><td>BayesWave deglitching</td></tr><tr><td>GW200115_042309</td><td>Livingston</td><td>BayesWave deglitching</td></tr><tr><td>GW200129_065458</td><td>Livingston</td><td>Linear subtraction</td></tr></tbody></table>

The duration of the data analyzed for each candidate is chosen such that the evolution of the signal from $f_{low}$ to merger and ringdown is captured, and that there is 2 s of data postmerger [4]. The overall likelihood of data from across the detector network is obtained by multiplying together the single-detector likelihoods for the given set of parameters.

As described in Appendix E 3, we marginalize over the uncertainty in the strain calibration. The frequency and phase calibration uncertainties are modeled using frequency-dependent splines. The coefficients of these splines are allowed to vary alongside the signal parameters with prior distributions on each spline node informed by the measured uncertainty at each node [131]. Preliminary studies [675,676] have shown that, given the SNR of the candidates during O3, the calibration systematic errors are expected to have negligible impact on the estimation of the astrophysical parameters.

## 1. Data-quality mitigation

For candidates affected by transient, non-Gaussian detector noise, as part of the event-validation process described in Sec. III B, we perform data-quality mitigation prior to performing source-parameter estimation, as summarized in Table XVI. Where possible, noise transients are modeled and subtracted with the BayesWave algorithm [377,379], or with the gwsubtract algorithm using a witness time series [44,59], as described in Appendix C. Such subtraction is first used to mitigate the effects of a glitch that appear in data from the LIGO Livingston detector overlapping GW170817 [126,677].

When analyzing Virgo data, the systematic error in calibration around 50 Hz described in Sec. III A is mitigated by setting the PSD to a large value ($1 \text{ Hz}^{-1/2}$) for 46–51 Hz, such that the affected data do not influence the results.

## 2. Waveforms

The waveform models used to analyze each candidate are selected depending upon the most likely source for the signal. Each candidate undergoes an initial parameter-estimation analysis shortly after the candidate is first identified. This is used to roughly infer the component masses (and other properties) of the binary source of the candidate signal, which are used to verify analysis settings. A further, more exhaustive set of parameter-estimation analyses are conducted to produce final results. To assess potential systematic uncertainties from waveform modeling, we perform analyses with two waveform families [131].

In cases with component masses in excess of $3M_{\odot}$, analyses are conducted using the SEOBNRv4PHM [137] and IMRPhenomXPHM [136] waveform models. The NRSur7dq4 NR surrogate model [678], previously used in a subset of analyses in GWTC-2 [3], is restricted in its length to only approximately 20 orbits before the merger, and so not generally applicable for analysis of the candidates in this catalog. The SEOBNRv4PHM waveform is part of the SEOBNR waveform family [625,663]. It is a time-domain model that is constructed by first deriving a time-dependent rotation from the coprecessing to the inertial frame using the EOB equations of motion [679,680] for the spins and orbital angular momentum, and then applying this rotation to the nonprecessing (incorporating only spins parallel to the orbital angular momentum) SEOBNRv4HM waveform. The SEOBNRv4HM model is computed by solving the EOB equations obtained by resumming PN corrections and incorporating information from NR simulations and BH perturbation theory [141]. To model spin precession, SEOBNRv4PHM numerically evolves the EOB dynamics of the system, including the spins in the time domain [137]. Since SEOBNRv4PHM inherits its higher-order multipole moment content from SEOBNRv4HM, it
includes the modes $(\ell, |m|) = \{(2, 2), (2, 1), (3, 3), (4, 4), (5, 5)\}$ in the coprecessing frame. The IMRPhenomXPHM model is the latest in the Phenom family of phenomenological, frequency-domain GW models, and is built upon the higher-order multipole model IMRPhenomXHM [140]. Each of the available higher-order multipole moments modeled in IMRPhenomXHM, $(\ell, |m|) = \{(2, 2), (2, 1), (3, 3), (3, 2), (4, 4)\}$, is tuned to NR and is rapidly generated through the use of frequency multibanding [681]. IMRPhenomXPHM includes precession effects by performing a frequency-dependent rotation on the nonprecessing GW waveform IMRPhenomXHM [140, 279, 363, 682, 683]. The angles used arise from a multiscale expansion of the PN equations of motion [291]. Neither waveform models the asymmetry between spherical harmonic modes with positive and negative spherical harmonic index $m$ [684], and neither is tuned to NR in the precessing sector, but both are validated by comparing to a large set of BBH waveforms [136, 137].

When the initial parameter estimation provides evidence that the secondary mass is below $3M_\odot$, then the signal may arise from a NSBH. In these cases, waveforms that include matter effects can be used to try to identify their imprint on the signal. We use the SEOBNRv4_ROM_NRTidalv2_NSBH [139] and IMRPhenomNSBH [138] waveforms. Both are nonprecessing, frequency-domain NSBH waveforms built upon previous nonprecessing, frequency-domain BBH waveform models: SEOBNRv4_ROM [625] for SEOBNRv4_ROM_NRTidalv2_NSBH, and a combination of the IMRPhenomC [283] amplitude and IMRPhenomD [685] phase for IMRPhenomNSBH. These models include corrections to the phase arising from matter effects as in IMRPhenomPv2_NRTidalv2, but have additional corrections to the amplitude tuned to NSBH NR waveforms.

For BBHs, the mass and spin of the final BH are calculated from the initial masses and spins using fits to NR results [237, 238, 304, 686, 687]. When using NSBH waveforms, the mass and spin of the final BH are calculated from the initial masses, the initial BH spin, and the NS tidal deformability $\Lambda_2$ using fits to NR results [688]. These fits are calibrated to BBH fits [238] in order to recover the BBH values in the test-mass limit ($m_2 \to 0$) and in the absence of tides ($\Lambda_2 \to 0$).

None of the waveform models employed for the analyses presented here include the effects of orbital eccentricity, and instead assume that all binaries follow quasicircular orbits. An eccentric source can be interpreted by a quasicircular analysis to be both higher mass and more equal mass than it truly is [393, 396–398, 689]. Consequently, if any sources analyzed here have eccentric orbits, their true masses may be lower and their mass ratios more unequal than our inferred values. Eccentricity may also influence the inferred spins [396–398, 690]. Significant eccentricity is not expected for the majority of sources considered here [97, 691].

### 3. Priors and sampling algorithms

To ensure that the parameter space for each candidate is explored adequately, each candidate is analyzed independently, with a choice of prior ranges for parameters that balance the required analysis time with the total volume of parameter space to be sampled. For all candidates, we choose a uniform prior over spin magnitudes and redshifted component masses, and an isotropic prior over spin orientation, sky location, and binary orientation [3, 14]. The default mass-ratio prior is $q \in [0.05, 1]$ to reflect the range of calibration for our waveform models [136, 137]. However, some candidates show strong support for mass ratios outside of this range (such as GW191219_163120). In these cases, we extend the priors, as biases due to any waveform inaccuracies are likely subdominant to those from truncating the prior, and we consider prior ranges as wide as $q \in [0.02, 1]$. Following GWTC-2 [3], we reweight posteriors to have a luminosity-distance prior corresponding to a uniform merger rate in the source's comoving frame for a Λ-cold-dark-matter cosmology with $H_0 = 67.9 \text{ km s}^{-1} \text{ Mpc}^{-1}$ and $\Omega_m = 0.3065$ [662].

We employ a number of different sampling techniques and their associated parameter-estimation pipelines for the candidate signals presented in this work. For the majority of candidates, the Bilby [144, 146] and RIFT [147–149] pipelines are used to generate samples from the posterior distributions for each signal.

Bilby provides support for both Markov-chain Monte Carlo samplers and nested sampling techniques [144]. We use the *Dynesty* [424] sampler, which uses nested sampling to sample the posterior probability distribution. Analyses are organized using *BilbyPipe* which enables greater automation and reproducibility of analysis pipeline construction [146]. We use *Bilby* for inferences using the *IMRPhenomXPHM* [136] model.

For candidates where more computationally expensive analyses are required, for example, using waveforms that include matter effects, we use the *Parallel Bilby* code [145]. This employs a highly parallel distributed approach to nested sampling that can be run over a large number of processing cores, reducing the wall time of the required computation.

To improve the sampling performance of *Bilby* and *Parallel Bilby*, the posterior distribution is analytically marginalized over luminosity distance [129] and geocenter time [146, 692] prior to sampling. We reconstruct posterior distributions for marginalized parameters in postprocessing: For each sample, we interpolate over a one-dimensional likelihood computed at discrete points within the prior of the marginalized parameter, and draw one value from this posterior probability curve [146, 150].

For time-domain, computationally expensive waveforms, we use *RIFT* [693]. This algorithm constructs the posterior probability distribution iteratively with two alternating steps. First, for a grid of intrinsic-parameter
points, a marginalized likelihood is evaluated by integrating over extrinsic parameters (source position, orientation, and coalescence time) [147]. From this discrete grid of likelihoods, a continuous likelihood distribution is constructed via Gaussian-process regression. A new grid is then sampled from the resulting posterior probability distribution; this process is repeated until convergence is reached. RIFT's grid-based approach has been shown to produce results consistent with our stochastic sampling algorithms [693].

To marginalize over calibration uncertainty [131,694], the calibration coefficients are sampled alongside the source parameters in inferences performed by Bilby and Parallel Bilby [146], whereas for RIFT, this marginalization is done using likelihood reweighting (with the same spline calibration model) after the inference of the source parameters [675].

All sampling algorithms return posterior samples in the same format, and these are postprocessed using PESUMMARY [425] to produce uniform HDF5 results. In the preparation of GWTC-2 [3], we employ some automation to assist with monitoring the parameter-estimation processes as they run. For GWTC-2.1 and GWTC-3, we further develop this automation into the Asimov [426] code. This allows the creation of analysis pipeline configurations to be fully automated, with the intention of ensuring consistency between analysis settings used for different algorithms.

The settings for the Bilby and RIFT analyses are designed to be as consistent as possible, aside from the differences in waveforms used. However, there do exist a number of differences between the analyses, such as the marginalization over time and the tapering applied to time-domain waveforms, that may lead to differences in results. Any differences should be negligible for intrinsic parameters such as the masses. In cases where the Bilby and RIFT parameters agree, we can be more confident in the robustness of results.

## APPENDIX F: UNCONFIRMED cWB-ONLY CANDIDATES

The minimally modeled cWB pipeline (described in Sec. IV B) can identify a range of signal morphologies, including signals unrelated to CBC sources [31]. Since cWB does not exploit the rich prior information provided by CBC waveform templates, its flexibility in identifying many potential signals comes with a reduced sensitivity to CBC signals that match such templates as compared to the matched-filter analyses. However, for the O3 analyses, we find that the efficiency of detection of cWB becomes comparable to that of matched-filter pipelines for systems with $(1+z)M \gtrsim 150M_\odot$, and it is possible for cWB to identify CBC signals that would otherwise be omitted from the candidate list. In selecting candidates for Table I, we use a criterion that the probability of astrophysical origin

assuming a CBC source is $p_{astro} > 0.5$; as explained in Sec. IV D, because we cannot assume that a candidate identified by the cWB pipeline is consistent with a CBC origin, we require independent support from a template-based search pipeline.

Here we discuss three candidates from cWB that would have $p_{astro} > 0.5$ assuming a CBC source, but for which we do not have the counterpart from the matched-filter search pipelines required to corroborate the CBC source assumption. The candidates 190804_083543 and 190930_234652 were found during O3a, and 200214_224526 was found during O3b. These three candidates have FAR < 2.0 yr⁻¹, meeting the threshold for marginal candidates. The candidate 190804_083543 was also studied in the O3 minimally modeled search for short-duration transient signals [31], and the candidate 200214_224526 was further studied in the O3 search for IMBH binaries [26]. In each case, we find that the analysis and interpretation of the data is made more difficult by the presence of glitches, as illustrated in Fig. 16. The detailed reconstructed signal morphology is shown in Fig. 17, which displays the time-frequency map [89,108]. For a CBC signal, we would typically expect the reconstructed signal to show a chirp from lower to higher frequencies, with higher-mass sources being limited to lower frequencies and shorter durations [109,657]. However, we find that the three candidates have a range of signal morphologies.

The candidate 190804_083543 was identified in low latency by the cWB BBH search analyzing HL network data, and in the offline analysis its SNR is 13.3 and FAR is 0.024 yr⁻¹. It occurs less than a second after a loud series of glitches in the LIGO Livingston detector. The time around these glitches is vetoed by a Burst category 2 flag that measures length sensing and control channels [63]. Similar sequences of glitches have been observed at other times for both the LIGO Livingston and LIGO Hanford detectors [695]. In O3, it was observed that times around these loud glitches produced a higher rate of background triggers in the cWB analysis, and we consider this candidate of likely instrumental origin.

The candidate 190930_234652 was identified in low latency by the cWB BBH search analyzing HL network data, and in the offline analysis its SNR is 8.6 and FAR is 1.0 yr⁻¹. Slow scattering glitches [69] are present in the LIGO Hanford data at the time of the candidate. These glitches correlate with the observed motion of the suspension systems and directly overlap the candidate. At LIGO Livingston, excess motion was measured by accelerometers at the time of the candidate that may also account for the observed signal in that detector's data. We consider this candidate of likely instrumental origin.

The candidate 200214_224526 was identified in low latency by the cWB BBH search analyzing HL network data, and in the offline analysis its SNR is 13.1 and FAR is 0.13 yr⁻¹. In LIGO Livingston, the candidate is associated
<figure><img src="image_19.png" /><figcaption>FIG. 16. Spectrograms [73] of data surrounding 190804_083543, 190930_234652, and 200214_224526. Time is plotted relative to the central time of each trigger. The plotted data are from LIGO Hanford for 190930_234652 and from LIGO Livingston for 190804_083543 and 200214_224526. The red box represents the bandwidth and duration of the candidate identified by cWB. In all three cases, the data are affected by transient noise at the time of the trigger, and additional excess power is present in the data that is not accounted for as part of the trigger identified by cWB. Although there is power present in the other detectors, the evidence for instrumental origin of the candidate in one detector makes it likely that this is just a chance coincidence.</figcaption></figure>

with a fast scattering glitch [69]; a sequence of such glitches is observed for multiple seconds before and after the candidate. As shown in Fig. 16, the glitch overlaps the candidate in LIGO Livingston. In LIGO Hanford, we find evidence of a weak scattering arch that starts approximately 0.5 s before the trigger and lasts approximately 2 s in the frequency range 20–30 Hz. The candidate was studied in the search for IMBH binaries [26], where it was listed as the third-ranked candidate (the first ranked being GW190521). However, it was not corroborated by any matched-filter search analysis, and it was concluded that the trigger was due to noise.

<figure><img src="image_20.png" /><figcaption>FIG. 17. The coherent-energy time-frequency maps of the three candidates identified by only the cWB analysis. These time-frequency maps are scalograms of the Wilson-Daubechies-Meyer wavelet transform of the candidate signal, where the scale is represented by frequency [89,108], for the coherent energy $E_c$ (see Appendix D 5). The normalization of the coherent energy scale is such that the sum of all the pixel values times their area is equal to the power SNR. The time axis corresponds to GPS times after adding the appropriate offset. For 190804_083543, the offset is 1 248 942 961 s, for 190930_234652, the offset is 1 253 922 430 s, and for 200214_224526, the offset is 1 265 755 544 s.</figcaption></figure>
For each of 190804_083543, 190930_234652, and 200214_224526 there is plausible evidence that the candidate is of instrumental origin. Regardless of the instrumental or astrophysical origin of these candidates, their morphologies (as shown in Fig. 17) do not resemble the CBC signals so far detected. The versatility of cWB in identifying potential signals without a template means that a variety of sources could be detected, such that the assumption of a CBC source is not assured and must be verified. Under the alternative assumption of a non-CBC source, the probability of astrophysical origin would be reduced, making any candidates less plausible as GW signals. Detection of new source types, and inference of their rates, would enable calculation of $p_{astro}$ for a range of sources in addition to CBCs.

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