Insights into the Milky Way pulsar--black hole population using radio and gravitational wave observations

The detection of two NS--BH mergers by LIGO-Virgo provided the first direct confirmation of the existence of this type of system in the Universe. These detections also imply the existence of pulsar--black hole (PSR--BH) systems. In this analysis, we use the non-detection of any PSR--BH systems in current radio surveys to estimate a 95\% upper limit of $\sim$150 PSR--BH binary systems that are beaming towards the Earth in the Milky Way. This corresponds to a 95\% upper limit of $\mathcal{R}_{\rm LIGO} = 7.6$~yr$^{-1}$ on the merger detection rate for the LIGO-Virgo network scaled to a range distance of 100~Mpc, which is consistent with the rates derived by LIGO-Virgo. In addition, for the first time, we use the merger detection rates estimate by LIGO-Virgo to predict the number of detectable PSR--BH systems in the Milky Way. We find there to be $\left< N_{\rm obs, NSBH, e} \right> = 2^{+5}_{-1}$ and $\left< N_{\rm obs, NSBH, p} \right> = 6^{+7}_{-4}$ detectable PSR--BH systems in the Milky Way corresponding to the event-based and population-based merger detection rates estimated by LIGO-Virgo respectively. We estimate the probability of detecting these PSR--BH systems with current radio pulsar surveys, showing that the Arecibo PALFA survey has the highest probability of detecting a PSR--BH system, while surveys with recently commissioned and planned telescopes are almost guaranteed to detect one of these systems. Finally, we discuss the hurdles in detecting PSR--BH systems and how these can be overcome in the future.