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The next generation of gravitational-wave observatories will achieve unprecedented strain sensitivities with an expanded observing band. They will detect $\mathcal{O}\left({10}^5\right)$binary neutron star (BNS) mergers every year, the loudest of which will be in the band for $\approx 90$minutes with signal-to-noise ratios $\approx 1500$. We show that subtleties arising from the rotation of the Earth and the free-spectral range of gravitational-wave interferometers dramatically increases the complexity of next-gen BNS signals compared to the one-minute signals seen by LIGO-Virgo. Reduced-order quadrature, a compression method currently relied upon to speed up the most expensive BNS calculations, may no longer be effective in determining the astrophysical parameters of next-gen BNS signals. We carry out reduced-order inference on a simulated next-gen BNS signal taking into account the Earth’s rotation and the observatories’ free-spectral range. We show that reduced-order modeling becomes impractical, and the full problem becomes computationally infeasible, when we include data below $\approx 16\mathrm{Hz}$—a part of the observing band that is critical for precise sky localization. We discuss potential paths toward solving this complex problem. 

As the catalogue of gravitational-wave transients grows, several entries appear ‘exceptional’ within the population. Tipping the scales with a total mass of $$\sim 150 \,{\rm M}_\odot$$, GW190521 likely contained black holes in the pair-instability mass gap. The event GW190814, meanwhile, is unusual for its extreme mass ratio and the mass of its secondary component. A growing model-building industry has emerged to provide explanations for such exceptional events, and Bayesian model selection is frequently used to determine the most informative model. However, Bayesian methods can only take us so far. They provide no answer to the question: does our model provide an adequate explanation for exceptional events in the data? If none of the models we are testing provide an adequate explanation, then it is not enough to simply rank our existing models – we need new ones. In this paper, we introduce a method to answer this question with a frequentist p-value. We apply the method to different models that have been suggested to explain the unusually massive event GW190521: hierarchical mergers in active galactic nuclei and globular clusters. We show that some (but not all) of these models provide adequate explanations for exceptionally massive events like GW190521. 

Abstract It has become increasingly useful to answer questions in gravitational-wave astronomy usingtransdimensionalmodels, where the number of free parameters can be varied depending on the complexity required to fit the data. Given the growing interest in transdimensional inference, we introduce a new package for the Bayesian inference Library (Bilby), calledtBilby. ThetBilbypackage allows users to set up transdimensional inference calculations using the existingBilbyarchitecture with off-the-shelf nested samplers and/or Markov Chain Monte Carlo algorithms. Transdimensional models are particularly helpful when seeking to test theoretically uncertain predictions described by phenomenological models. For example, bursts of gravitational waves can be modeled using a superposition ofNwavelets, whereNis itself a free parameter. Short pulses are modeled with small values ofN, whereas longer, more complicated signals are represented with a large number of wavelets stitched together. Other transdimensional models have been used to describe instrumental noise and the population properties of gravitational-wave sources. We provide a few demonstrations oftBilby, including fitting the gravitational-wave signal GW150914 with a superposition ofNsine-Gaussian wavelets. We outline our plans to further develop thetBilbycode suite for a broader range of transdimensional problems. 

It has become increasingly useful to answer questions in gravitational-wave astronomy using transdimensional models where the number of free parameters can be varied depending on the complexity required to fit the data. Given the growing interest in transdimensional inference, we introduce a new package for the Bayesian inference Library (Bilby) called tBilby. The tBilby package allows users to set up transdimensional inference calculations using the existing Bilby architecture with off-the-shelf nested samplers and/or Markov Chain Monte Carlo algorithms. Transdimensional models are particularly helpful when we seek to test theoretically uncertain predictions described by phenomenological models. For example, bursts of gravitational waves can be modelled using a superposition of N wavelets where N is itself a free parameter. Short pulses are modelled with small values of N whereas longer, more complicated signals are represented with a large number of wavelets stitched together. Other transdimensional models have found use describing instrumental noise and the population properties of gravitational-wave sources. We provide a few demonstrations of tBilby, including fitting the gravitational-wave signal GW150914 with a superposition of N sine-Gaussian wavelets. We outline our plans to further develop the tbilby code suite for a broader range of transdimensional problems. 

Abstract Many astronomical surveys are limited by the brightness of the sources, and gravitational-wave searches are no exception. The detectability of gravitational waves from merging binaries is affected by the mass and spin of the constituent compact objects. To perform unbiased inference on the distribution of compact binaries, it is necessary to account for this selection effect, which is known as Malmquist bias. Since systematic error from selection effects grows with the number of events, it will be increasingly important over the coming years to accurately estimate the observational selection function for gravitational-wave astronomy. We employ density estimation methods to accurately and efficiently compute the compact binary coalescence selection function. We introduce a simple pre-processing method, which significantly reduces the complexity of the required machine-learning models. We demonstrate that our method has smaller statistical errors at comparable computational cost than the method currently most widely used allowing us to probe narrower distributions of spin magnitudes. The currently used method leaves 10%–50% of the interesting black hole spin models inaccessible; our new method can probe >99% of the models and has a lower uncertainty for >80% of the models. 

Abstract Ultralight bosons are a proposed solution to outstanding problems in cosmology and particle physics: they provide a dark-matter candidate while potentially explaining the strong charge-parity problem. If they exist, ultralight bosons can interact with black holes through the superradiant instability. In this work we explore the consequences of this instability on the evolution of hierarchical black holes within dense stellar clusters. By reducing the spin of individual black holes, superradiance reduces the recoil velocity of merging binary black holes, which, in turn, increases the retention fraction of hierarchical merger remnants. We show that the existence of ultralight bosons with mass 2 × 10 −14 ≲ μ /eV ≲ 2 × 10 −13 would lead to an increased rate of hierarchical black hole mergers in nuclear star clusters. An ultralight boson in this energy range would result in up to ≈60% more present-day nuclear star clusters supporting hierarchical growth. The presence of an ultralight boson can also double the rate of intermediate-mass black hole mergers to ≈0.08 Gpc −3 yr −1 in the local universe. These results imply that a select range of ultralight boson masses can have far-reaching consequences for the population of black holes in dense stellar environments. Future studies into black hole cluster populations and the spin distribution of hierarchically formed black holes will test this scenario. 

Abstract Active galactic nuclei (AGNs) are promising environments for the assembly of merging binary black hole (BBH) systems. Interest in AGNs as nurseries for merging BBHs is rising, following the detection of gravitational waves from a BBH system from the purported pair-instability mass gap, most notably GW190521. AGNs have also been invoked to explain the formation of the high-mass-ratio system GW190814. We draw on simulations of BBH systems in AGNs to propose a phenomenological model for the distribution of black hole spins of merging binaries in AGN disks. The model incorporates distinct features that make the AGN channel potentially distinguishable from other channels, such as assembly in the field and in globular clusters. The model parameters can be mapped heuristically to the age and density of the AGN disks. We estimate the extent to which different populations of mergers in AGNs can be distinguished. If the majority of merging black holes are assembled in AGNs, future gravitational-wave observations may provide insights into the dynamics of AGN disks. 

ABSTRACT The detection of an intermediate-mass black hole population (102–106 M⊙) will provide clues to their formation environments (e.g. discs of active galactic nuclei, globular clusters) and illuminate a potential pathway to produce supermassive black holes. Ground-based gravitational-wave detectors are sensitive to mergers that can form intermediate-mass black holes weighing up to ∼450 M⊙. However, ground-based detector data contain numerous incoherent short duration noise transients that can mimic the gravitational-wave signals from merging intermediate-mass black holes, limiting the sensitivity of searches. Here, we follow-up on binary black hole merger candidates using a ranking statistic that measures the coherence or incoherence of triggers in multiple-detector data. We use this statistic to rank candidate events, initially identified by all-sky search pipelines, with lab-frame total masses ≳ 55 M⊙ using data from LIGO’s second observing run. Our analysis does not yield evidence for new intermediate-mass black holes. However, we find support for eight stellar-mass binary black holes not reported in the first LIGO–Virgo gravitational wave transient catalogue GWTC-1, seven of which have been previously reported by other catalogues.