One Small Step for $Roman$; One Giant Leap for Black Holes

The $Roman$ microlensing program can detect and fully characterize black holes (BHs) that are in orbit with about 30 million solar-type and evolved stars with periods up to the mission lifetime $P<T=5$ yr, and semi-major axes $a>0.2$au, i.e., $P> 10$ d $(M/M_\odot)^{-1/2}$, where $M$ is the BH mass. For BH companions of about 150 million later (fainter) main-sequence stars, the threshold of detection is $a>0.2$ au $\times 10^{(H_{\rm Vega}-18.5)/5}$. The present $Roman$ scheduling creates a "blind spot" near periods of $P=3.5$ yr due to a 2.3-year gap in the data. It also compromises the characterization of BHs in eccentric orbits with periods $P>3$ yr and peribothra within a year of the mission midpoint. I show that one can greatly ameliorate these issues by making a small adjustment to the $Roman$ observing schedule. The present schedule aims to optimize proper-motion measurements, but the adjustment proposed here would degrade these by only 4%-9%. For many cases of $P>90$ d BHs, there will be discrete and/or continuous degeneracies. For G-dwarf and evolved sources, it will be straightforward to resolve these by radial-velocity (RV) follow-up observations, but such observations will be more taxing for fainter sources. Many BH-binaries in orbits of 5 yr $<P<10$ yr will be reliably identified as such from the $Roman$ data, but will lack precise orbits. Nevertheless, the full orbital solutions can be recovered by combining $Roman$ astrometry with RV followup observations. BH binaries with periods 10 yr $<P<$ 95 yr $(M/10 M_\odot)^{1/4}$ can be detected from their astrometric acceleration, but massive multi-fiber RV monitoring would be needed to distinguish them from the astrophysical background due to stellar binaries.