The accumulation of certain types of dark matter particles in neutron star cores due to accretion over long timescales can lead to the formation of a mini black hole. In this scenario, the neutron star is destabilized and implodes to form a black hole without significantly increasing its mass. When this process occurs in neutron stars in coalescing binaries, one or both stars might be converted to a black hole before they merge. Thus, in the mass range of $\sim 1–2M_{\odot }$, the Universe might contain three distinct populations of compact binaries: one containing only neutron stars, the second population of only black holes, and a third, mixed population consisting of a neutron star and a black hole. However, it is unlikely to have a mixed population as the various timescales allow for both neutron stars to remain or collapse within a short timescale. In this paper, we explore the capability of future gravitational-wave detector networks, including upgrades of Advanced LIGO and Virgo, and new facilities such as the Cosmic Explorer and Einstein Telescope (XG network), to discriminate between different populations by measuring the effective tidal deformability of the binary, which is zero for binary black holes but nonzero for binary neutron stars. Furthermore, we show that observing the relative abundances of the different populations can be used to infer the timescale for neutron stars to implode into black holes, and in turn, provide constraints on the particle nature of dark matter. The XG network will infer the implosion timescale to within an accuracy of 0.01 Gyr at 90% credible interval and determine the dark matter mass and interaction cross section to within a factor of 2 GeV and $10{\mathrm{cm}}^{-2}$, respectively.

• Received 2 November 2022
• Accepted 4 April 2023

DOI:https://doi.org/10.1103/PhysRevD.107.083037