Deep learning and Bayesian inference of gravitational-wave populations: Hierarchical black-hole mergers

Abstract

The catalog of gravitational-wave events is growing, and so are our hopes of constraining the underlying astrophysics of stellar-mass black-hole mergers by inferring the distributions of, e.g., masses and spins. While conventional analyses parametrize this population with simple phenomenological models, we propose an emulation-based approach that can compare astrophysical simulations against gravitational-wave data. We combine state-of-the-art deep-learning techniques with hierarchical Bayesian inference and exploit our approach to constrain the properties of repeated black-hole mergers from the gravitational-wave events in the most recent LIGO/Virgo catalog. Deep neural networks allow us to (i) construct a flexible single-channel population model that accurately emulates simple parametrized numerical simulations of hierarchical mergers, (ii) estimate selection effects, and (iii) recover the branching ratios of repeated-merger generations. Among our results, we find the following: The distribution of host-environment escape speeds favors values less than $100\mathrm{km}{\mathrm{s}}^{-1}$ but is relatively flat, with around $37\%$ of first-generation mergers retained in their host environments; first-generation black holes are born with a maximum mass that is compatible with current estimates from pair-instability supernovae; there is multimodal substructure in both the mass and spin distributions, which, in our model, can be explained by repeated mergers; and binaries with a higher-generation component make up at least $14\%$ of the underlying population. Though these results are inferred through emulation of a simplified model, the deep-learning pipeline we present is readily applicable to realistic astrophysical simulations

29 pages, 17 figures, 5 tables. Accepted in PRD

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• Blind spots and biases: the dangers of ignoring eccentricity in gravitational-wave signals from binary black holes
• Evidence for the evolution of black hole mass function with redshift
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• Reconstructing the Genealogy of LIGO-Virgo Black Holes
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• Evidence of the pair instability gap from black hole masses
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