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The population properties of intermediate-mass black holes remain largely unknown, and understanding their distribution could provide a missing link in the formation of supermassive black holes and galaxies. Gravitational-wave observations can help fill in the gap from stellar mass black holes to supermassive black holes with masses between ∼100–10⁴M_⊙. In our work, we propose a new method for examining lens populations through lensing statistics of gravitational waves, here focusing on inferring the number density of intermediate-mass black holes through hierarchical Bayesian inference. Simulating ∼200 lensed gravitational-wave signals, we find that existing gravitational-wave observatories at their design sensitivity could either constrain the number density of 10⁶Mpc⁻³within a factor of 10, or place an upper bound of ≲10⁴Mpc⁻³if the true number density is 10³Mpc⁻³. More broadly, our method leaves room for incorporation of additional lens populations, providing a general framework for probing the population properties of lenses in the universe.

 

Third-generation (3G) gravitational-wave detectors will observe thousands of coalescing neutron star binaries with unprecedented fidelity. Extracting the highest precision science from these signals is expected to be challenging owing to both high signal-to-noise ratios and long-duration signals. We demonstrate that current Bayesian inference paradigms can be extended to the analysis of binary neutron star signals without breaking the computational bank. We construct reduced order models for ∼90minute long gravitational-wave signals, covering the observing band (5−2048Hz), speeding up inference by a factor of ∼1.3×10^4 compared to the calculation times without reduced order models. The reduced order models incorporate key physics including the effects of tidal deformability, amplitude modulation due to the Earth's rotation, and spin-induced orbital precession. We show how reduced order modeling can accelerate inference on data containing multiple, overlapping gravitational-wave signals, and determine the speedup as a function of the number of overlapping signals. Thus, we conclude that Bayesian inference is computationally tractable for the long-lived, overlapping, high signal-to-noise-ratio events present in 3G observatories. 

Gravitational-wave astrophysics has the potential to be transformed by a global network of longer, colder, and thus more sensitive detectors. This network must be constructed to address a wide range of science goals, involving binary coalescence signals as well as signals from other, potentially unknown, sources. It is crucial to understand which network configurations---the number, type, and location of the detectors in the network---can best achieve these goals. In this work we examine a large number of possible three-detector networks, variously composed of Voyager, Einstein Telescope, and Cosmic Explorer detectors, and evaluate their performance against a number of figures of merit meant to capture a variety of future science goals. From this we infer that network performance, including sky localization, is determined most strongly by the type of detectors contained in the network, rather than the location and orientation of the facilities.