Distinguishing Neutron Star vs. Low-Mass Black Hole Binaries with Late Inspiral & Postmerger Gravitational Waves $-$ Sensitivity to Transmuted Black Holes and Non-Annihilating Dark Matter

Gravitational wave signals from binary neutron star (BNS) mergers and binary low-mass black hole (BLMBH) mergers are highly similar in the early inspiral phase. Consequently, the astrophysical origin of recently detected low-mass compact binary coalescences has remained ambiguous, particularly in the absence of electromagnetic counterparts. In this work, we demonstrate that proposed detectors with increased high-frequency sensitivity $-$ including NEMO, Cosmic Explorer, and the Einstein Telescope $-$ will reliably distinguish these two source classes in the late inspiral and postmerger regimes. We further show how these detections can be used to disentangle the individual contributions of BNS and BLMBH systems to the compact binary merger rate, while accounting for misclassification probabilities. Finally, we show this can lead to constraints on the interaction of heavy, non-annihilating dark matter with nucleons. This is achieved by noting that capture of such dark matter particles into neutron stars would lead to transmuted black holes (TBHs), formed via neutron star collapse, which would contribute to the BLMBH rate.