Empirical determination of the Galactic neutron star--black hole merger rate using StarTrack models

Abstract: The discovery of a pulsar in a binary system with a black hole would provide a unique laboratory for testing general relativity in the strong-field regime and offer vital constraints on massive star evolution. We assess prospects for the detectability of such systems by utilizing the radio pulsar population and survey models within the modeling package PsrPopPy and, as a proof of principle, two evolutionary models with different treatments of common-envelope phases from the stellar population synthesis code StarTrack. For these two models, assuming the radio pulsar beaming model proposed by Tauris and Manchester and accounting for the effects of orbital motion on pulsar detectability, we calculate upper limits on the number of neutron star--black hole systems in the Galaxy and the corresponding merger rate given the lack of any radio-detected pulsar--black hole binary systems in current radio surveys. For the most constraining model, we find a Galactic merger rate $&lt; 4.3~\text{Myr}<sup>{-1}$ (at 95\% confidence). These results are extrapolated to the expected horizon distance for the fifth LIGO observing run, leading to LIGO detection rate estimates that are consistent with the latest values reported by the LIGO-Virgo-KAGRA collaboration. Our results indicate that the increased sensitivity of FAST, MeerKAT, and DSA offers the best prospects yet for uncovering this elusive population.