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The astrophysical origin of over 90 compact binary mergers discovered by the LIGO and Virgo gravitational wave observatories is an open question. While the unusual mass and spin of some of the discovered objects constrain progenitor scenarios, the observed mergers are consistent with multiple interpretations. A promising approach to solve this question is to consider the observed distributions of binary properties and compare them to expectations from different origin scenarios. Here we describe a new hierarchical population analysis framework to assess the relative contribution of different formation channels simultaneously. For this study we considered binary formation in active galactic nucleus (AGN) disks along with phenomenological models, but the same framework can be extended to other models. We find that high-mass and high-mass-ratio binaries appear more likely to have an AGN origin compared to having the same origin as lower-mass events. Future observations of high-mass black hole mergers could further disentangle the AGN component from other channels.

Binary neutron star mergers (NSMs) have been confirmed as one source of the heaviest observable elements made by the rapid neutron-capture (r-) process. However, modeling NSM outflows—from the total ejecta masses to their elemental yields—depends on the unknown nuclear equation of state (EOS) that governs neutron star structure. In this work, we derive a phenomenological EOS by assuming that NSMs are the dominant sources of the heavy element material in metal-poor stars withr-process abundance patterns. We start with a population synthesis model to obtain a population of merging neutron star binaries and calculate their EOS-dependent elemental yields. Under the assumption that these mergers were responsible for the majority ofr-process elements in the metal-poor stars, we find parameters representing the EOS for which the theoretical NSM yields reproduce the derived abundances from observations of metal-poor stars. For our proof-of-concept assumptions, we find an EOS that is slightly softer than, but still in agreement with, current constraints, e.g., by the Neutron Star Interior Composition Explorer, withR_1.4= 12.25 ± 0.03 km andM_TOV= 2.17 ± 0.03M_⊙(statistical uncertainties, neglecting modeling systematics).