Astrometric microlensing probes of the isolated neutron star population with Roman

Notoriously hard to detect and study, isolated neutron stars (NS) could provide valuable answers to fundamental questions about stellar evolution and explosion physics. With the upcoming Roman Space Telescope, scheduled for launch in 2026, a new and powerful channel for their detection - astrometric microlensing - will become available. We set out to create a realistic sample of simulated gravitational microlensing events as observed by Roman with the Galactic Bulge Time Domain Survey. We focus in particular on the population of NS lenses, which has until now been largely understudied. We use state-of-the-art Galactic models tailored for application to microlensing by compact objects. We simulate four different NS populations with Maxwellian natal kick distributions: $\bar{v} = (150, \ 250, \ 350, \ 450)$ km/s. We apply projected Roman precision, cadence, and detectability criteria. We find the parameter space $\log_{10} t_{\rm E}$ - $\log_{10} θ_{\rm E}$, which will be accessible to Roman observations, to be maximally efficient for classification of stellar remnants. We find a feature in this space that is characteristic to NS; using this feature, optimal samples of NS candidates can be constructed from Roman-like datasets. We describe the dependence of observable parameter distributions on the assumed mean kick velocities. As the effects of natal kicks are very complex and mutually counteracting, we suggest more detailed studies focused on the dynamics of NS are needed in anticipation of Roman and future surveys. We estimate Roman will observe approximately $11\,000$ microlensing events - including $\sim100$ with NS lenses - whose both photometric and astrometric signal are detectable; the event yield decreases by $38\%$ if gap-filling low-cadence observations are not included. We make all simulated microlensing event datasets publicly available in preparation for Roman data.