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S. Appert

Publications and source records attributed to S. Appert.

At least 19 recordsLinked to original sources

Updated Upper Limits on the Isotropic Gravitational-Wave Background from LIGO, Virgo, and KAGRA Data through April 2025

We report results from a search for an isotropic stochastic gravitational-wave background using data collected by the LIGO--Virgo--KAGRA Collaboration. The analysis uses data from the first observing run through April 1, 2025, during the fourth observing run. New frequency-domain cuts are implemented to address a class of non-stationary spectral noise features that were not effectively identified and mitigated by existing data-quality checks in past analyses. Consequently, previously analyzed data from the fourth observing run are re-processed with the updated cuts. We find no evidence for a stochastic background signal and place upper limits on the gravitational-wave energy density. In particular, for a background following a power law with spectral index 2/3 as predicted by inspiralling compact binaries, we find $\Omega_\mathrm{GW}(25\,\mathrm{Hz}) \leq 2.0 \times 10^{-9}$, while scale-invariant backgrounds are constrained to $\Omega_\mathrm{GW}(25\,\mathrm{Hz}) \leq 2.8 \times 10^{-9}$, both at the 95\% credible level for a log-uniform prior on $\Omega_\mathrm{GW}$. Relative to the constraints from previous data recomputed with the new frequency-domain cuts, these limits improve by a factor of 1.4. We also update bounds on alternative gravity scenarios predicting non-standard polarization modes, and we verify that correlated magnetic noise sources remain below the sensitivity of this search. Combining these observational constraints with population models of compact binary coalescences informed by the latest gravitational-wave transient catalog, GWTC-5.0, we predict the amplitude of the compact binary background to be $\Omega_\mathrm{CBC}(25\,\mathrm{Hz}) = 6.3^{+5.0}_{-2.2} \times 10^{-10}$ at the 90\% credible level.

gr-qc

Constraints on ultralight bosons from merging binary and remnant black holes observed during the second and third parts of the fourth LIGO-Virgo-KAGRA observing run

We present constraints on ultralight bosons using binary black hole mergers observed in the second and third parts of the fourth LIGO-Virgo-KAGRA observing run. Directed searches are conducted for long-transient gravitational waves from ultralight vector boson clouds around merger remnants, using a hidden-Markov-model (HMM) tracking scheme. We target the remnant black holes formed in the binary coalescences that produced GW250114 and GW250207. We find no evidence for such signals from either target. Estimating our search sensitivity at a threshold corresponding to a 1% false alarm probability, we thus disfavor vector boson masses in the range of $[2.80, 3.95]\times 10^{-13}$ eV with greater than 90% confidence. In addition, we derive constraints on ultralight scalar and vector bosons from the inferred high spins of the constituent black holes in three binaries, using events GW240515, GW241113, and GW241225_08. The excluded mass ranges in this approach depend on the assumed black-hole ages. At $10^5$ years, corresponding to typical dynamically formed binaries, we exclude scalar and vector bosons in the ranges $[1.39, 6.94]\times 10^{-13}$ eV and $[0.32, 14.4]\times 10^{-13}$ eV at 90% confidence, respectively.

gr-qc

LIGO A$^\sharp$: Detector Design and Science Prospects Beyond A+

We present the LIGO A$^\sharp$ detector concept, an upgrade for the LIGO observatories based on room-temperature interferometers beyond the fifth observing run (O5). Building on the A+ sensitivity, A$^\sharp$ targets broadband sensitivity improvements through heavier test masses, improved suspensions and seismic isolation, increased arm-cavity power, enhanced frequency-dependent squeezing, reduced coating thermal noise considering two scenarios, and improved control of mechanical motion and optical modes. We describe the principal design choices, projected noise performance, and corresponding astrophysical prospects. LIGO A$^\sharp$ substantially increases compact-binary detection rates, strengthens population inference, and improves both early-warning times and localization for binary neutron star mergers. The improved sensitivity enables more detailed studies of compact-binary coalescences, including higher-order multipoles, intermediate-mass black holes, remnant black hole ringdown, and the neutron star equation of state. It also broadens the discovery potential for new gravitational-wave sources such as continuous waves and bursts, should enable detection of the stochastic background from compact binary mergers if it remains undetected after O5, and strengthens the role of gravitational-wave detectors as probes of fundamental physics. We discuss key technical challenges and the role of A$^\sharp$ as both a major scientific upgrade for the 2030s and a technology pathfinder for next-generation gravitational-wave observatories, such as Cosmic Explorer.

astro-ph.IM

LIGO Detector Characterization in the Second and Third Parts of the Fourth Observing Run

LIGO detector characterization efforts enabled the confident detection of gravitational waves from hundreds of compact binary coalescences during the fourth observing run. Reliable production of high quality detector data and rapid noise mitigation efforts allow the extraction of the most in-depth knowledge of gravitational wave sources and their progenitors. In this paper we describe LIGO detector characterization activities during the second and third parts of O4-O4b and O4c. We summarize changes in detector configuration and performance at the LIGO Hanford and LIGO Livingston Observatories between the end of the first part of O4a and the end of O4c, including upgrades made during the commissioning break preceding O4b and during repairs performed in O4c. We describe instrumental investigations carried out at both sites designed to understand and subsequently mitigate the effect on detector sensitivity of transient glitches, narrowband spectral lines, and vibration-driven noise, among other data quality concerns. We then review the tools and procedures used to validate gravitational wave candidates and the data quality products thus supplied to searches for gravitational waves from compact binary coalescences and unmodeled transients, continuous gravitational waves, and the stochastic gravitational wave background. The efforts of the detector characterization group are essential for maintaining and improving the sensitivity and reliability of the LIGO detectors especially as observing runs lengthen and more events are detected. We conclude with prospects for LIGO detector characterization activities in future observing runs.

astro-ph.IM

GWTC-5.0: Tests of General Relativity

The signals from the LIGO-Virgo-KAGRA network of gravitational-wave (GW) detectors allow us to perform sensitive tests of general relativity (GR) in the dynamical and strong-field regime of gravity. We present the results of seven tests of GR using the observed binary signals in the fifth GW Transient Catalog (GWTC-5.0), i.e., up to and including the second part of the fourth observing run (O4b). We restrict our analysis to the confident signals, henceforth called events, observed by at least two detectors that have estimated false alarm rates $\le 10^{-3} \ \rm{yr}^{-1}$. These include 72 events from O4b and five events from the first part of the fourth observing run that are now analyzed due to their increased significance from updated search results, bringing the total number of events for tests of GR in the cumulative GWTC to 168. After subtracting the best-fit waveforms, we find the residuals are consistent with detector noise for all events considered. We also find no strong evidence for additional polarizations beyond those predicted by GR. We perform tests of GW generation, improving the constraints on deviations from the GR post-Newtonian coefficients by factors of 1.2-2.6. Finally, we find overall consistency of the remnants with GR using both time- and frequency-domain methods. For GW240621_195059, postmerger data are consistent with the dominant quadrupolar ($\ell=|m|=2$) mode of a Kerr black hole and its first overtone, with spurious high-frequency content preventing a spectroscopic constraint of GR. In the frequency-domain ringdown analysis, the GR prediction lies in the tails of the combined results, possibly due to the limited catalog size. However, the combined results indicate improved consistency with GR over GWTC-4.0, owing to the contribution of GW250114 with a network matched-filter signal-to-noise ratio of 76.9. Overall, we find no evidence for physics beyond GR.

gr-qc

Sub-Torque-Balance Upper Limits on Continuous Gravitational Waves from Scorpius X-1

We present the results of a search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1 using LIGO data from the first part of the fourth LIGO-Virgo-KAGRA observing run. By applying the resampling version of the cross-correlation pipeline to search for signal frequencies $f_0$ between $25$ and $200\un{Hz}$ (corresponding to neutron star spin frequencies of $12.5$ to $100\un{Hz}$ for GW due to triaxiality, or $\sim15-20$ to $\sim120-150\un{Hz}$ for GW due to $r$-modes), we set upper limits below the standard torque balance level, independent of neutron star spin inclination, for $50\un{Hz}\lesssim f_0\lesssim200\un{Hz}$. While uncertainties in the modelling of torque and equation of state limit the strength of our inference, our results nonetheless argue against torque balance in this spin range for a neutron star described by a hadronic equation of state. The most sensitive upper limits on the gravitational wave amplitude $h_0$, at the upper end of the frequency band searched, approach $5\times10^{-26}$ marginalized over inclination angle and $2\times10^{-26}$ assuming the most favorable inclination. The marginalized upper limits correspond to a sensitivity depth of $70-75\un{Hz}^{-1/2}$, improving sensitivity considerably over previous searches. Expressed as constraints on the triaxial deformation of the neutron star, the limits correspond to an ellipticity of $3\times10^{-5}$ if the GW frequency $f_0$ is $75\un{Hz}$ and $3\times10^{-6}$ if $f_0=200\un{Hz}$, approaching deformations which could be supported by ordinary nuclear matter. Outliers from the search were ruled out as potential signals by a combination of hierarchical followup and analysis of additional data from later in the observing run.

astro-ph.HE

Narrow spectral artifact investigation and mitigation in LIGO data from the fourth LIGO-Virgo-KAGRA observing run

We present efforts to identify, characterize, and mitigate narrow spectral artifacts in LIGO detector data during the fourth LIGO-Virgo-KAGRA observing run. Narrow spectral artifacts in gravitational-wave detectors are non-astrophysical noise sources that can degrade searches for narrowband persistent gravitational waves. Identifying and, where possible, mitigating these noise sources is one of the core efforts of the LIGO Detector Characterization group. Key software tools have been updated and new tools deployed for the fourth LIGO-Virgo-KAGRA observing run to facilitate investigations and data monitoring. We discuss these tool upgrades, and present several identified narrowband artifacts that have been successfully investigated and mitigated in LIGO data. Regardless of whether artifacts are mitigated or not, narrowband persistent gravitational-wave searches require information on which frequency bands contain non-astrophysical artifacts. Minimizing the number of bands containing non-astrophysical artifacts is essential to maximize the potential for discovery of a new class of gravitational-wave signals.

astro-ph.IM

Open Data from LIGO, Virgo, and KAGRA through the Second Part of the Fourth Observing Run

LIGO, Virgo, KAGRA, and GEO 600 form a network of gravitational-wave observatories. Data and analysis results from this network are made publicly available through the Gravitational Wave Open Science Center (GWOSC). This paper describes open data from this network, including the addition of data from the second part of the fourth observing run (O4b) and selected periods from the preceding engineering run (ER16), which were collected from times spanning April 6th, 2024 to January 28th, 2025. The public data set includes calibrated strain time series for each instrument, data from additional channels used for noise subtraction and detector characterization, and new analysis data products in the online GWOSC release associated with version 5.0 of the Gravitational-Wave Transient Catalog.

gr-qc

GWTC-5.0: An Introduction to Version 5.0 of the Gravitational-Wave Transient Catalog

The Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational-wave signals identified by the LIGO-Virgo-KAGRA Collaboration in gravitational-wave data produced by the eponymous detectors. The catalog provides information about the identified candidates, such as the arrival time and amplitude of the signal and properties of the signal's source as inferred from the observational data. GWTC is the release of this dataset and version 5.0 extends the catalog to include observations made during the second part of the fourth LIGO-Virgo-KAGRA observing run up until 2025 January 28. This paper marks an introduction to a collection of articles related to this version of the catalog, GWTC-5.0. This update significantly increases the number of detected merging binary systems of black holes and neutron stars to over 300, enabling many follow-up studies toward understanding the gravitational-wave universe. The collection of articles accompanying the catalog provides documentation of the methods used to analyze the data, summaries of the catalog of events, observational measurements drawn from the population, and detailed discussions of selected candidates.

gr-qc

GWTC-5.0: Methods for Identifying and Characterizing Gravitational-wave Transients

The Gravitational-Wave Transient Catalog (GWTC) is a collection of candidate gravitational-wave transient signals identified and characterized by the LIGO-Virgo-KAGRA Collaboration. Producing the contents of the GWTC from detector data requires complex analysis methods. These comprise techniques to model the signal; identify the transients in the data; evaluate the quality of the data and mitigate possible instrumental issues; infer the parameters of each transient; compare the data with the waveform models for compact binary coalescences, and handle the large amount of results associated with all these different analyses. In this paper, we describe the methods employed to produce the catalog's fifth release, GWTC-5.0, focusing on the analysis of the second part of the fourth observing run of LIGO, Virgo and KAGRA.

gr-qc

GWTC-5.0: Observations from the Second Part of the Fourth LIGO-Virgo-KAGRA Observing Run and Updates to the Gravitational-Wave Transient Catalog

Version 5.0 of the Gravitational-Wave Transient Catalog (GWTC-5.0) adds new candidates detected by the LIGO Virgo KAGRA network of observatories through the second part of the fourth observing run (O4b: 2024 April 10 15:00:00 to 2025 January 28 17:00:00 UTC) and four days of the preceding engineering run (2024 April 6 to 2024 April 10). We find 161 compact binary coalescence candidates that are identified by at least one of our search algorithms with a probability of astrophysical origin $p_\mathrm{astro} \geq 0.5$ and that are not vetoed during event validation. We also provide detailed source property measurements for 104 candidates that have a false-alarm rate < 1yr$^{-1}$. Based on the inferred component masses, all these candidates are consistent with signals from binary black holes. Median inferred component masses in the new candidates range from 5.14$M_\odot$ (GW241109_115924) to 70$M_\odot$ (GW241116_151753). Improvements in detector sensitivity allow us to observe compact binary coalescences with increasing clarity: 5 binary-black-hole signals have network signal-to-noise ratio exceeding 30, with a maximum to date of 76.9 for GW250114_082203. Such loud signals enable more precise studies of properties of their astrophysical sources and tests of general relativity. We also present updated results up to the first part of the fourth observing run, identifying 229 candidates. This brings the total number of transients in the cumulative GWTC having $p_\mathrm{astro} \geq 0.5$ to 390, further expanding the size of the catalog and our view of the gravitational-wave universe.

gr-qc

GWTC-5.0: Population Properties of Merging Compact Binaries

We present the population properties of merging compact binaries inferred using 267 mergers from the cumulative Gravitational-Wave Transient Catalog 5.0. As this data set contains no new sources with a neutron star, we primarily focus on the properties of the binary black hole mergers. We infer the merger rate of binary black holes with component masses between $2.5\,\mathrm{M}_\odot $ and $200\,\mathrm{M}_\odot $ to be $27.5\text{--} 49.4 \, \mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ (all intervals at $90\%$ credible levels) at redshift $z = 0.2$. We find evidence for a subpopulation of binary black hole mergers that host a rapidly spinning black hole (dimensionless spins $\chi \sim 0.7$), consistent with signatures of hierarchical mergers. We find that these occur at two mass scales, the first at primary masses $\sim 10$--$20\,\mathrm{M}_\odot $ and the second above $\sim 45\,\mathrm{M}_\odot $, and we estimate their total rate at $z=0.2$ to be $0.2\text{--} 3.11 \, {\rm Gpc}^{-3} {\rm yr}^{-1}$. We infer that, above $40\,\mathrm{M}_\odot $, the mass distribution of the less massive (secondary) black hole declines more steeply than that of the more massive (primary) one. This is consistent with a flatter mass-ratio distribution and indicates the prevalence of unequal-mass binaries with large primary masses. We find evidence for two features in the black hole mass spectrum: a peak around $10\,\mathrm{M}_\odot $ and a change of slope at around $35\,\mathrm{M}_\odot $. Black holes of $\sim 35\,\mathrm{M}_\odot $ pair preferentially with companions of similar mass. Additionally, we find that the effective inspiral spin distribution of binary black holes is asymmetric about zero, based on which we infer that at least $9 \%$ of mergers occur in channels with some preference for spin-orbit alignment. We find evidence that...

astro-ph.HE

GWTC-5.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation

We employ 236 gravitational-wave (GW) sources in the fifth LIGO--Virgo--KAGRA Collaboration (LVK) Gravitational-Wave Transient Catalog (GWTC-5.0) to estimate the Hubble constant $H_0$. We compare the luminosity distance measured from GWs to the redshift inferred i) using features in the mass spectrum, and ii) using statistical host galaxy association. Probing the relationship between source luminosity distances and redshifts obtained in this way yields constraints on cosmological parameters. We estimate $H_0 = {71.7}_{-7.5}^{+9.4}\,{\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}}$ (median with $68\%$ symmetric credible interval). This combines information from the source-frame mass distribution with the $H_0$ measurement from GW170817 and its electromagnetic counterpart as well as galaxy catalog information from Dark Energy Survey Year 6 (DES-Y6). We improve over the GWTC-4.0 measurement by using more GW sources, some with significantly smaller sky localization volumes, which leads to a reduction by $22.0\%$ of the $H_0$ uncertainty and a reconstructed mass distribution with lower uncertainties. We also constrain deviations from general relativity (GR) which affect GW propagation, specifically that modify the luminosity distance inferred from the GW signal. We find no departures from GR in parameterized tests of GW propagation.

astro-ph.CO

GW240925 and GW250207: Astrophysical Calibration of Gravitational-wave Detectors

GW240925 and GW250207 are two loud gravitational-wave signals from binary black hole coalescences observed with network signal-to-noise ratios $\sim 32$ and $\sim 69$, respectively, by the LIGO Hanford--LIGO Livingston--Virgo network. Gravitational-wave signals from coalescing binaries have characteristic phase and amplitude evolution predicted by general relativity. These signal waveforms, together with measured instrumental calibration uncertainties, are used to infer source parameters. However, for sufficiently loud detections it is possible to constrain the calibration of the detectors directly using the signals themselves. We present the first informative astrophysical measurements of gravitational-wave detector calibration. For GW240925, we verify the inference of Hanford calibration from the astrophysical signal through cross-checks with known calibration errors obtained from in-situ measurements. At the time of GW250207, the Hanford detector was not fully stabilized, leading to elevated calibration uncertainties; thus, astrophysical calibration is essential to obtain accurate data and to enable source localization. These well-localized, high signal-to-noise observations have the potential to offer precise measurements of source properties, stringent tests of general relativity, and informative dark siren measurements, provided that calibration uncertainties are properly incorporated. As detector sensitivity improves, astrophysical calibration will become an increasingly valuable complement to in-situ calibration measurements. Obtaining accurate calibration will be essential for precision gravitational-wave science.

gr-qc

Searches for Binary Mergers with Sub-solar Mass Components in Data from the First Part of LIGO--Virgo--KAGRA's Fourth Observing Run

We report on a gravitational wave search for compact binary coalescences involving at least one component with mass between $0.2\,M_\odot$ to $1\,M_\odot$, and ratio of component masses between 0.1 and 1. The analysis uses data collected by the LIGO detectors between May 24 2023 15:00 UTC and January 16 2024 16:00 UTC. No statistically significant sub-solar mass candidates were identified by the participating search algorithms. We report the detection sensitivity of the current searches to the target sub-solar mass black hole population. With the absence of detections, we place upper limits on the merger rate of sub-solar mass black holes, ranging from 110 ${\rm Gpc^{-3}\,yr^{-1}}$ to 10000 ${\rm Gpc^{-3}\,yr^{-1}}$ at 90\% confidence. We constrain two illustrative dark matter scenarios that can form sub-solar mass compact objects with these searches: primordial black holes, and dark black holes forming in a dissipative dark matter model. For late-forming primordial black hole binaries, our search excludes the fraction of dark matter in primordial black holes to be $\leq 1$ only for masses above $0.9\,M_\odot$. In the early-formation scenario, we limit this fraction to be $\leq 7\%$ at $1\,M_\odot$, and $\leq 40\%a$ at $0.35\,M_\odot$. For the dissipative model, the excluded region in the parameter space of dark matter fraction in dark black holes and their minimum possible mass extends down to (0.9 to 1.2) $\times 10^{-5}$ at $1\,M_\odot$ with no constraints below $0.02\,M_\odot$. For the first time, we report the detection sensitivity of our searches to binaries with sub-solar mass neutron stars, and place the 90\% confidence merger rate limit at (570 to 710) ${\rm Gpc^{-3}\,yr^{-1}}$ for a population with component masses distributed uniformly down to $0.5\,M_\odot$.

astro-ph.HE

Searches for Continuous Gravitational Waves from Supernova Remnants in the first part of the LIGO-Virgo-KAGRA Fourth Observing run

We present results from directed searches for continuous gravitational waves from a sample of 15 nearby supernova remnants, likely hosting young neutron star candidates, using data from the first eight months of the fourth observing run (O4) of the LIGO-Virgo-KAGRA Collaboration. The analysis employs five pipelines: four semi-coherent methods -- the Band-Sampled-Data directed pipeline, Weave and two Viterbi pipelines (single- and dual-harmonic) -- and PyStoch, a cross-correlation-based pipeline. These searches cover wide frequency bands and do not assume prior knowledge of the targets' ephemerides. No evidence of a signal is found from any of the 15 sources. We set 95\% confidence-level upper limits on the intrinsic strain amplitude, with the most stringent constraints reaching $\sim 4 \times 10^{-26}$ near 300 Hz for the nearby source G266.2$-$1.2 (Vela Jr.). We also derive limits on neutron star ellipticity and $r$-mode amplitudes for the same source, with the best constraints reaching $\lesssim 10^{-7}$ and $\lesssim 10^{-5}$, respectively, at frequencies above 400 Hz. These results represent the most sensitive wide-band directed searches for continuous gravitational waves from supernova remnants to date.

gr-qc

Narrowband searches for continuous gravitational waves from known pulsars in the first two parts of the fourth LIGO--Virgo--KAGRA observing run

Rotating non-axisymmetric neutron stars (NSs) are promising sources for continuous gravitational waves (CWs). Such CWs can, if detected, inform us about the internal structure and equation of state of NSs. Here, we present a narrowband search for CWs from known pulsars, for which an efficient and sensitive matched-filter search can be applied. Narrowband searches are designed to be robust to mismatches between the electromagnetic (EM) and gravitational emissions, in contrast to fully targeted searches where the CW emission is assumed to be phase-locked to the EM one. In this work, we search for the CW counterparts emitted by 34 pulsars using data from the first and second parts of the fourth LIGO--Virgo--KAGRA observing run. This is the largest number of pulsars so far targeted for narrowband searches in the advanced detector era. We use the 5n-vector narrowband pipeline, which applies frequency-domain matched filtering. In previous searches, it covered a narrow range in the frequency -- frequency time derivative ($f$ -- $\dot{f}$) space. Here, we also explore a range in the second time derivative of the frequency $\ddot{f}$ around the value indicated by EM observations. Additionally, for the first time, we target sources in a binary system with this kind of search. We find no evidence for CWs and therefore set upper limits on the strain amplitude emitted by each pulsar, using simulated signals added in real data. For 20 analyses, we report an upper limit below the theoretical spin-down limit. The tightest constraint is for pulsar PSR J0534+2200 (the Crab pulsar), for which our strain upper limit on the CW amplitude is $\lesssim 2\%$ of its spin-down limit, corresponding to less than $0.04\%$ of the spin-down power being radiated in the CW channel.

gr-qc

GWTC-4.0: Tests of General Relativity. I. Overview and General Tests

The worldwide LIGO-Virgo-KAGRA network of gravitational-wave (GW) detectors continues to increase in sensitivity, thus increasing the quantity and quality of the detected GW signals from compact binary coalescences. These signals allow us to perform ever-more sensitive tests of general relativity (GR) in the dynamical and strong-field regime of gravity. This paper is the first of three, where we present the results of a suite of tests of GR using the binary signals included in the fourth GW Transient Catalog (GWTC-4.0), i.e., up to and including the first part of the fourth observing run of the detectors (O4a). We restrict our analysis to the 91 confident signals, henceforth called events, that were measured by at least two detectors, and have false alarm rates $\le 10^{-3} \mathrm{yr}^{-1}$. These include 42 events from O4a. This first paper presents an overview of the methods, selection of events and GR tests, and serves as a guidemap for all three papers. Here we focus on the four general tests of consistency, where we find no evidence for deviations from our models. Specifically, for all the events considered, we find consistency of the residuals with noise. The final mass and final spin as inferred from the low- and high-frequency parts of the waveform are consistent with each other. We also find no evidence for deviations from the GR predictions for the amplitudes of subdominant GW multipole moments, or for non-GR modes of polarization. We thus find that GR, without new physics beyond it, is still consistent with these GW events. The results of the two additional papers in this trio also find overall consistency with vacuum GR, with more than 90% of the events being consistent with GR at the 90% credible level. While one of the ringdown analyses finds the GR value in the tails for its combined results, this may be due in part to catalog variance.

gr-qc