Modelling neutron star-black hole binaries: future pulsar surveys and gravitational wave detectors

Binaries comprised of a neutron star (NS) and a black hole (BH) have so far eluded observations as pulsars and with gravitational waves (GWs). We model the formation and evolution of these NS+BH binaries - including pulsar evolution - using the binary population synthesis code COMPAS. We predict the presence of a total of 50-2000 binaries containing a pulsar and a BH (PSR+BHs) in the Galactic field. We find the population observable by the next generation of radio telescopes, represented by the SKA and MeerKAT, current (LIGO/Virgo) and future (LISA) GW detectors. We conclude that the SKA will observe 1-80 PSR+BHs, with 0-4 binaries containing millisecond pulsars. MeerKAT is expected to observe 0-40 PSR+BH systems. Future radio detections of NS+BHs will constrain uncertain binary evolution processes such as BH natal kicks. We show that systems in which the NS formed first (NSBH) can be distinguished from those where the BH formed first (BHNS) by their pulsar and binary properties. We find 40 per cent of the LIGO/Virgo observed NS+BHs from a Milky Way like field population will have a chirp mass ≥3.0 M_⊙. We estimate the spin distributions of NS+BHs with two models for the spins of BHs. The remnants of BHNS mergers will have a spin of ~0.4, whilst NSBH merger remnants can have a spin of ~0.6 or ~0.9 depending on the model for BH spins. We estimate that approximately 25-1400 PSR+BHs will be radio alive whilst emitting GWs in the LISA frequency band, raising the possibility of joint observation by the SKA and LISA.