  Neutron star-black hole (NSBH) mergers detected in gravitational waves have
the potential to shed light on supernova physics, the dense matter equation of
state, and the astrophysical processes that power their potential
electromagnetic counterparts. We use the population of four candidate NSBH
events detected in gravitational waves so far with a false alarm rate $\leq
1~\mathrm{yr}^{-1}$ to constrain the mass and spin distributions and
multimessenger prospects of these systems. We find that the black holes in
NSBHs are both less massive and have smaller dimensionless spins than those in
black hole binaries. We also find evidence for a mass gap between the most
massive neutron stars and least massive black holes in NSBHs at 98.6%
credibility. Using an approach driven by gravitational-wave data rather than
binary simulations, we find that fewer than 14% of NSBH mergers detectable in
gravitational waves will have an electromagnetic counterpart. While the
inferred presence of a mass gap and fraction of sources with a counterpart
depend on the event selection and prior knowledge of source classification, the
conclusion that the black holes in NSBHs have lower masses and smaller spin
parameters than those in black hole binaries is robust. Finally, we propose a
method for the multimessenger analysis of NSBH mergers based on the
nondetection of an electromagnetic counterpart and conclude that, even in the
most optimistic case, the constraints on the neutron star equation of state
that can be obtained with multimessenger NSBH detections are not competitive
with those from gravitational-wave measurements of tides in binary neutron star
mergers and radio and X-ray pulsar observations.
