Challenges in Forming Millisecond Pulsar-Black Holes from Isolated Binaries

Binaries harboring a millisecond pulsar (MSP) and a black hole (BH) are a key observing target for current and upcoming pulsar surveys. We model the formation and evolution of such binaries in isolation at solar metallicity using the next-generation binary population synthesis code POSYDON. We examine neutron star (NS)-BH binaries where the NS forms first (labeled NSBH), as the NS must be able to spin-up to MSP rotation periods before the BH forms in these systems. We find that NSBHs are very rare and have a birth rate < 1 Myr$^{-1}$ for a Milky Way-like galaxy in our typical models. The NSBH birth rate is 2-3 orders of magnitude smaller than that for NS-BHs where the BH forms first (labeled BHNS). These rates are also sensitive to model assumptions about the supernova (SN) remnant masses, natal kicks, and common-envelope efficiency. We find that 100% of NSBHs undergo a mass ratio reversal before the first SN and up to 64% of NSBHs undergo a double common envelope phase after the mass ratio reversal occurs. Most importantly, no NSBH binaries in our populations undergo a mass transfer phase, either stable or unstable, after the first SN. This implies that there is no possibility of pulsar spin-up via accretion, and thus MSP-BH binaries cannot form. Thus, dynamical environments and processes may provide the only formation channels for such MSP-BH binaries.