The degree of black-hole spin-orbit misalignment ("tilts") in the astrophysical population could be a powerful diagnostic to distinguish between binary formation in isolation, in dynamical environments, or in hierarchical triples. However, robust population-level spin tilt measurements are complicated by model misspecification as well as numerical and Poisson variance, ultimately owing to poor single-event constraints on tilts. Motivated by reports of a possible peak in the spin tilt distribution, we analyze the fourth LIGO-Virgo-KAGRA gravitational-wave transient catalog to test for preferred spin orientations at different black hole masses. We find that a peak in spin tilts is not statistically significant nor model independent. Since the data cannot be used to reliably identify subpopulations based on their spin tilt properties, we also consider a complementary approach: measuring the spin magnitude and tilt distributions at fixed mass scales. We find no confident correlation between mass and spin tilt, but we do confirm a confident correlation between spin magnitude and mass, corroborating recent analyses.

As gravitational-wave catalogs grow, they will become increasingly computationally expensive to analyze in their entirety, especially when inferring astrophysical source populations with high-dimensional, flexible models. Bayesian statistics offers a natural remedy, letting us update our knowledge of physical models as new data arrive, without re-analyzing existing data. However, doing so requires the posterior probability density of model parameters for previous observations, which is typically intractable. Here, we use variational neural posterior estimation to rapidly update the inferred population of binary black holes as data are observed in gravitational-wave detectors. We apply this approach to real and simulated catalogs analyzed with both low- and high-dimensional population models, testing the reliability of three update cadences: with new catalogs of sources, month by month during an observing run, and as each new signal arrives. We investigate the success and failure modes of neural sequential updates, finding that the robustness of updating is sensitive to the information contained in each update and that updating is most effective when performed with larger segments of data. We outline one additional scientific application enabled by Bayesian updating: identification of events that are individually informative about the population. Neural Bayesian updates to astrophysical population models also provide efficient likelihood representations for joint analyses with other data, e.g., standard-siren cosmology, and similar methods can be used to perform Bayesian stochastic background searches.

The origins of merging compact binaries observed by the LIGO-Virgo-KAGRA gravitational-wave detectors remain uncertain, with multiple astrophysical channels possibly contributing to the merger rate. Formation processes can imprint nontrivial correlations in the underlying distribution of source properties, but current understanding of the overall population relies heavily on simplified and uncorrelated parametric models. In this work, we use PixelPop-a high-resolution Bayesian nonparametric model with minimal assumptions-to analyze multidimensional correlations in the astrophysical distribution of masses, spins, and redshifts of black-hole mergers from mock gravitational-wave catalogs constructed using population-synthesis simulations. With full parameter estimation on 400 detections at current sensitivities, we show explicitly that neglecting population-level correlations biases inference. In contrast, modeling all significant correlations with PixelPop allows us to correctly measure the astrophysical merger rate across all source parameters. We then propose a nonparametric method to distinguish between different formation channels by comparing the PixelPop results back to astrophysical simulations. For our simulated catalog, we find that only formation channels with significantly different physical processes are distinguishable, whereas channels that share evolutionary stages are not. Given the substantial uncertainties in source formation, our results highlight the necessity of multidimensional astrophysics-agnostic models like PixelPop for robust interpretation of gravitational-wave catalogs.

Repeated black-hole mergers in dense stellar clusters are a plausible mechanism to populate the predicted gap in black hole masses due to the pair-instability supernova process. These hierarchical mergers carry distinct spin characteristics relative to first-generation black holes. We introduce an astrophysically motivated model in the joint space of effective inspiral and precessing spins, which captures the dominant spin dynamics expected for hierarchical mergers. We find decisive evidence for a transition at m_{1}=46.2_{-7.2}^{+12.6}M_{⊙}, above which the population is nearly entirely hierarchical, a location consistent with the anticipated onset of the pair-instability gap. We also infer a global peak in the hierarchical merger rate at m_{1}=15.7_{-1.1}^{+3.2}M_{⊙}. The existence of low- and high-mass subpopulations of higher-generation black holes suggests the contribution of both near-solar-metallicity and metal-poor star clusters to the hierarchical merger population. Our results reinforce the growing evidence for detailed, mass-dependent substructure in the spin distribution of the binary black hole population.

Pair-instability supernovae leave behind no compact remnants, resulting in a predicted gap in the distribution of stellar black-hole masses. Gravitational waves from binary black-hole mergers probe the relevant mass range and analyses of the LIGO-Virgo-KAGRA catalog (GWTC-4) indicate a possible mass cutoff at 40-50Mo. However, the robustness of this result remains unclear. To this end, using full Bayesian parameter estimation, we simulate gravitational-wave catalogs with and without such a mass cutoff and then test whether its presence or absence is correctly inferred with parametric population models. For catalogs similar to GWTC-4, confident identification of a cutoff is not guaranteed, but the best constraints among our simulations are compatible with results from GWTC-4 when the model includes a cutoff. Conversely, spurious identification of a cutoff is unlikely. For catalogs expected by the end of the O4 observing run, uncertainty in the cutoff mass is reduced by >= 20%, but a cutoff at 40-50Mo yields only a lower bound on the 12C(alpha; gamma)16O reaction rate, our most stringent constraints on the S factor at 300 keV being S300 >= 125 keV b at 90% credibility. Relative uncertainties on the Hubble parameter H0 from gravitational-wave data alone can still be up to 100%. We also analyze GWTC-4 with the nonparametric PIXELPOP population model, finding that some mass features are more prominent than in parametric models but a sharp cutoff is not required. However, the parametric model passes a likelihood-based predictive test in GWTC-4 and the PIXELPOP results are consistent with those from our simulated catalogs with a cutoff. Such tests are necessary to make astrophysical claims from gravitational-wave catalogs.

From catalogs of gravitational-wave transients, the population-level properties of their sources and the formation channels of merging compact binaries can be constrained. However, astrophysical conclusions can be biased by misspecification or misestimation of the population likelihood. Despite detection thresholds on the false-alarm rate (FAR) or signal-to-noise ratio (SNR), the current catalog is likely contaminated by noise transients. Further, computing the population likelihood becomes less accurate as the catalog grows. Current methods to address these challenges often scale poorly with the number of events and potentially become infeasible for future catalogs. Here, we evaluate a simple remedy: increasing the significance threshold for including events in population analyses. To determine the efficacy of this approach, we analyze simulated catalogs of up to 1600 gravitational-wave signals from black-hole mergers using full Bayesian parameter estimation with current detector sensitivities. We show that the growth in statistical uncertainty about the black-hole population, as we analyze fewer events but with higher SNR, depends on the source parameters of interest. When the SNR threshold is raised from 11 to 15-reducing our catalog size by two-thirds-we find that statistical uncertainties on the mass distribution only grow by a few 10% and constraints on the spin distribution are essentially unchanged; meanwhile, uncertainties on the high-redshift cosmic merger rate more than double. Simultaneously, numerical uncertainty in the estimate of the population likelihood more than halves, allowing us to ensure unbiased inference without additional computational expense. Our results demonstrate that focusing on higher-significance events is an effective way to facilitate robust astrophysical inference with growing gravitational-wave catalogs.

Next-generation gravitational-wave observatories will reach farther into the universe than currently possible, revealing black-hole mergers from early stellar binary systems such as Population III stars, whose properties are currently poorly constrained. We develop a method to infer the properties of their progenitor populations from gravitational-wave catalogs. Using Bayesian deep learning, we train an emulator for population-synthesis predictions of black-hole merger properties across redshift as a function of the initial stellar mass function, crucially accounting for systematic uncertainty due to the finite number of training simulations. Combined with a nonparametric model for star formation history, we analyze catalogs containing both Population I/II and III sources simulated with full Bayesian parameter estimation for a detector network of Cosmic Explorer and Einstein Telescope with one year of observing time. We demonstrate our ability to separate these two populations at high redshifts where both make comparable contributions to the black-hole merger rate, excluding a Population III merger rate of zero at nearly 100% credibility. Moreover, we can place meaningful constraints on the Population III progenitor distributions; in particular, we constrain the spectral index of the initial mass function to within roughly +/-0.5 of the true value and the log of the star formation rate density to within ~25% over redshifts 10 to 20. By leveraging astrophysics-informed and astrophysics-agnostic models, we demonstrate the discriminative power of our combined inference approach and highlight the potential of next-generation gravitational-wave observatories to uncover the details of high-redshift stellar populations.

Gravitational-wave (GW) detections of electromagnetically bright compact binary coalescences can provide an independent measurement of the Hubble constant H 0 . In order to obtain a measurement that could help arbitrating the existing tension on H 0 , one needs to fully understand any source of systematic biases for this approach. In this study, we aim at understanding the impact of instrumental calibration errors (CEs) and uncertainties on luminosity distance measurements, D L , and the inferred H 0 results.We simulate binary neutron star mergers (BNSs), as detected by a network of Advanced LIGO and Advanced Virgo interferometers at their design sensitivity. We artificially add CEs equal to exceptionally large values experienced in LIGO-Virgo’s third observing run (O3). We find that for individual BNSs at a network signal-to-noise ratio of 50, the systematic errors on D L – and hence H 0 – are still smaller than the statistical uncertainties. The biases become more significant when we combine multiple events to obtain a joint posterior on H 0 . In the rather unrealistic case that the data around each detection is affected by the same CEs corresponding to the worst offender of O3, the true H 0 value would be excluded from the 90% credible interval after ∼ 40 sources. If instead 10% of the sources suffer from severe CEs, the true value of H 0 is included in the 90% credible interval even after we combine 100 sources.

Formation channels of merging compact binaries imprint themselves on the distributions and correlations of their source parameters, but current understanding of this population is hindered by simplified parametric models. We overcome such limitations using PixelPop [J. Heinzel, M. Mould, S. Alvarez-Lopez, and S. Vitale, companion paper, Phys. Rev. D 111, 063403 (2025)]-our Bayesian nonparametric multidimensional population model. We analyze data from the first three LIGO-Virgo-KAGRA observing runs and make high resolution, minimally modeled measurements of the pairwise distributions of binary black hole masses, redshifts, and spins. We find no evidence that the mass spectrum evolves over redshift and show that such measurements are fundamentally limited by the detector horizon. We find support for correlations of the spin distribution with binary mass ratio and redshift, but at reduced significance compared to overly constraining parametric models. Confident data-driven conclusions about population-level correlations with flexible models like PixelPop will require more informative gravitational-wave catalogs.

We present the results of a search for gravitational-wave transients associated with core-collapse supernova SN 2023ixf, which was observed in the galaxy Messier 101 via optical emission on 2023 May 19, during the LIGO–Virgo–KAGRA 15th Engineering Run. We define a five-day on-source window during which an accompanying gravitational-wave signal may have occurred. No gravitational waves have been identified in data when at least two gravitational-wave observatories were operating, which covered ∼14% of this five-day window. We report the search detection efficiency for various possible gravitational-wave emission models. Considering the distance to M101 (6.7 Mpc), we derive constraints on the gravitational-wave emission mechanism of core-collapse supernovae across a broad frequency spectrum, ranging from 50 Hz to 2 kHz, where we assume the gravitational-wave emission occurred when coincident data are available in the on-source window. Considering an ellipsoid model for a rotating proto-neutron star, our search is sensitive to gravitational-wave energy 1 × 10 −4 M ⊙ c 2 and luminosity 2.6 × 10 −4 M ⊙ c 2 s −1 for a source emitting at 82 Hz. These constraints are around an order of magnitude more stringent than those obtained so far with gravitational-wave data. The constraint on the ellipticity of the proto-neutron star that is formed is as low as 1.08, at frequencies above 1200 Hz, surpassing past results.

Measuring the distribution of spin tilts-the angles between the spin vectors and the binary orbital angular momentum-in stellar-mass binary black holes detected by LIGO-Virgo-KAGRA would provide valuable insight into their astrophysical origins. Analyses of the 69 binary black holes detected through LIGO-Virgo-KAGRA's third observing run yielded model-dependent conclusions, particularly regarding whether the spin tilt distribution exhibits a peak near alignment, as expected for binaries formed in galactic fields. In this work, we simulate populations of up to 1500 binary black hole systems with parameters consistent with the default GWTC-3 analysis, while introducing a correlation that favors small spin tilts for binaries with mass ratios near unity. We find that: (a) spurious peaks away from perfect alignment are possible even with catalogs of up to 300 sources; (b) establishing a definitive peak at alignment remains difficult even with 1500 detections; (c) integrated measurements-such as the fraction of events with tilt angles smaller than 10 degrees or greater than 90 degrees-are more robust and should be preferred, achieving relative 90% credible uncertainties of 20% - 80% with 1500 sources; and (d) even with the largest simulated catalogs, evidence for a mass ratio-tilt correlation remains inconclusive. Our results suggest that identifying the formation channels of merging black holes using spin tilts will remain challenging, but that model-independent measurements may yield more informative insights over model parameters themselves.

We present results from a search for X-ray/gamma-ray counterparts of gravitational-wave (GW) candidates from the third observing run (O3) of the LIGO-Virgo-KAGRA network using the Swift Burst Alert Telescope (Swift-BAT). The search includes 636 GW candidates received with low latency, 86 of which have been confirmed by the offline analysis and included in the third cumulative Gravitational-Wave Transient Catalogs (GWTC-3). Targeted searches were carried out on the entire GW sample using the maximum-likelihood Non-imaging Transient Reconstruction and Temporal Search pipeline on the BAT data made available via the GUANO infrastructure. We do not detect any significant electromagnetic emission that is temporally and spatially coincident with any of the GW candidates. We report flux upper limits in the 15-350 keV band as a function of sky position for all the catalog candidates. For GW candidates where the Swift-BAT false alarm rate is less than 10(-3) Hz, we compute the GW-BAT joint false alarm rate. Finally, the derived Swift-BAT upper limits are used to infer constraints on the putative electromagnetic emission associated with binary black hole mergers.

The origins of merging compact binaries observed by gravitational-wave detectors remains highly uncertain. Several astrophysical channels may contribute to the overall merger rate, with distinct formation processes imprinted on the structure and correlations in the underlying distributions of binary source parameters. In the absence of confident theoretical models, the current understanding of this population mostly relies on simple parametric models that make strong assumptions and are prone to misspecification. Recent work has made progress using more flexible nonparametric models, but detailed measurement of the multidimensional population remains challenging. In pursuit of this, we present PixelPop-a high resolution Bayesian nonparametric model to infer joint distributions and parameter correlations with minimal assumptions. PixelPop densely bins the joint parameter space and directly infers the merger rate in each bin, assuming only that bins are coupled to their nearest neighbors. We demonstrate this method on mock populations with and without bivariate source correlations, employing several statistical metrics for information gain and correlation significance to quantify our nonparametric results. We show that PixelPop correctly recovers the true populations within posterior uncertainties and offers a conservative assessment of population-level features and parameter correlations. Its flexibility and tractability make it a useful data-driven tool to probe gravitational-wave populations in multiple dimensions.

The LIGO-Virgo-KAGRA catalog has been analyzed with an abundance of different population models due to theoretical uncertainty in the formation of gravitational-wave sources. To expedite model exploration, we introduce an efficient and accurate variational Bayesian approach that learns the population posterior with a normalizing flow and serves as a drop-in replacement for existing samplers. With hardware acceleration, inference takes just seconds for the current set of black-hole mergers and readily scales to larger catalogs. The trained posteriors provide an arbitrary number of independent samples with exact probability densities, unlike established stochastic sampling algorithms, while requiring up to three orders of magnitude fewer likelihood evaluations and as few as O(103). Provided the posterior support is covered, discrepancies can be addressed with smoothed importance sampling, which quantifies a goodness-of-fit metric for the variational approximation while also estimating the evidence for Bayesian model selection. Neural variational inference thus enables interactive development, analysis, and comparison of population models, making it a useful tool for astrophysical interpretation of current and future gravitational-wave observations.

A precise characterization of the magnetic properties of LISA Pathfinder free falling test-masses is of special interest for future gravitational wave observatory in space. Magnetic forces have an important impact on the instrument sensitivity in the low frequency regime below the millihertz. In this paper we report on the magnetic injection experiments performed throughout LISA Pathfinder operations. We show how these experiments allowed a high precision estimate of the instrument magnetic parameters. The remanent magnetic moment was found to have a modulus of (0.245 + 0.081) nAm2, the x-component of the background magnetic field within the test masses position was measured to be (414 + 74) nT and its gradient had a value of (-7.4 + 2.1) mu T/m. Finally, we also measured the test mass magnetic susceptibility at 5 mHz to be (-3.3723 + 0.0069) x 10-5. All results are in agreement with on-ground estimates.

LISA Pathfinder was a mission designed to test key technologies required for gravitational wave detection in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime, which corresponds to the measurement band of interest for future space-borne gravitational wave observatories. Magnetically induced forces couple to the test mass motion, introducing a contribution to the relative acceleration noise between the free-falling test masses. In this Letter we present the first complete estimate of this term of the instrument performance model. Our results set the magnetic-induced acceleration noise during the February 2017 noise run of 0.25_{-0.08}^{+0.15}  fm s^{-2}/sqrt[Hz] at 1 mHz and 1.01_{-0.24}^{+0.73}  fm s^{-2}/sqrt[Hz] at 0.1 mHz. We also discuss how the nonstationarities of the interplanetary magnetic field can affect these values during extreme space weather conditions.

The coming years of gravitational wave astrophysics promises thousands of new detections, which can unlock fundamental scientific insights if the information in each observation can be properly synthesized into a coherent picture. State-of-the-art approaches often accomplish this with hierarchical Bayesian inference. However, this typically relies on Monte Carlo approximations that are already very expensive in current data, and may become prohibitively so in the future. In this paper we show how this process can be understood from a first-principles statistical approach. We derive an error estimator Ê for quantifying the amount of information that is lost due to the Monte Carlo approximation and recommend that this error is limited to no more than Ê≲ 0.2 bits for reliable inference. We also show that the hierarchical likelihood estimator is biased but may be corrected. Finally, we show some practical examples for inference on synthetic gravitational-wave population inference, demonstrating that simple models with strong assumptions can be much more stable to Monte Carlo uncertainty than those with weaker assumptions. We also provide a -installable package with which analysts can calculate the error statistics Ê.

The LISA Pathfinder (LPF) mission successfully demonstrated the feasibility of the technology needed for the future space borne gravitational wave observatory LISA. A key subsystem under study was the laser interferometer, which measured the changes in relative distance in between two test masses (TMs). It achieved a sensitivity of 32.0 thorn 2.4 -1.7 fm=ffiffiffiffiffiA/Hz, which was significantly better than the prelaunch tests. This improved performance allowed direct observation of the influence of laser frequency noise in the readout. The differences in optical path lengths between the measurement and reference beams in the individual interferometers of our setup determined the level of this undesired readout noise. Here, we discuss the dedicated experiments performed on LPF to measure these differences with high precision. We reached differences in path length difference between (368 +/- 5) mu m and (329.6 +/- 0.9) mu m which are significantly below the required level of 1 mm or 1000 mu m. These results are an important contribution to our understanding of the overall sensor performance. Moreover, we observed varying levels of laser frequency noise over the course of the mission. We provide evidence that these do not originate from the laser frequency stabilization scheme which worked as expected. Therefore, this frequency stabilization would be applicable to other missions with similar laser frequency stability requirements.

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) searches for gamma-ray/X-ray counterparts to gravitational wave (GW) candidate events identified during the third observing run of the Advanced LIGO and Advanced Virgo detectors. Using Fermi-GBM on-board triggers and sub-threshold gamma-ray burst (GRB) candidates found in the Fermi-GBM ground analyses, the Targeted Search and the Untargeted Search, we investigate whether there are any coincident GRBs associated with the GWs. We also search the Swift-BAT rate data around the GW times to determine whether a GRB counterpart is present. No counterparts are found. Using both the Fermi-GBM Targeted Search and the Swift-BAT search, we calculate flux upper limits and present joint upper limits on the gamma-ray luminosity of each GW. Given these limits, we constrain theoretical models for the emission of gamma-rays from binary black hole mergers.

Electrostatic force actuation is a key component of the system of geodesic reference test masses (TM) for the LISA orbiting gravitational wave observatory and in particular for performance at low frequencies, below 1 mHz, where the observatory sensitivity is limited by stray force noise. The system needs to apply forces of order 10$^{-9}$ N while limiting fluctuations in the measurement band to levels approaching 10$^{-15}$ N/Hz$^{1/2}$. We present here the LISA actuation system design, based on audio-frequency voltage carrier signals, and results of its in-flight performance test with the LISA Pathfinder test mission. In LISA, TM force actuation is used to align the otherwise free-falling TM to the spacecraft-mounted optical metrology system, without any forcing along the critical gravitational wave-sensitive interferometry axes. In LISA Pathfinder, on the other hand, the actuation was used also to stabilize the TM along the critical $x$ axis joining the two TM, with the commanded actuation force entering directly into the mission's main differential acceleration science observable. The mission allowed demonstration of the full compatibility of the electrostatic actuation system with the LISA observatory requirements, including dedicated measurement campaigns to amplify, isolate, and quantify the two main force noise contributions from the actuation system, from actuator gain noise and from low frequency ``in band'' voltage fluctuations. These campaigns have shown actuation force noise to be a relevant, but not dominant, noise source in LISA Pathfinder and have allowed performance projections for the conditions expected in the LISA mission.