Detecting isolated stellar-mass black holes by the Roman telescope

Isolated Stellar-Mass BlackHoles (ISMBHs) are potentially discernible through microlensing observations. In this work, we study detecting and characterizing ISMBHs with the Roman observations. We simulate a big ensemble of these events as seen by Roman and estimate the errors in the physical parameters of the lens objects, including their masses, distances, and proper motions through calculating Fisher and Covariance matrices. Since the ~2.3-year time gap between Roman's first three observing seasons and the others may lower the efficiency of realizing microlensing events and characterizing ISMBHs, we additionally consider a scenario where we add a small amount of additional observations -- one hour of observations every 10 days when the Bulge is observable during the large time gap -- which is equivalent to a total of about one additional day of observations with the Roman telescope. These extra observations increase Roman's efficiency for characterizing ISMBHs by ~$1-2\%$ and, more importantly, improve the robustness of the results by avoiding possible degenerate solutions. By considering uniform, and power-law mass functions ($dN/dM ~ M^{-\alpha}$, $\alpha=2,~1,~0.5$) for ISMBHs in the range of $[2,~50] M_{\odot}$, we conclude that the Roman telescope will determine the physical parameters of the lenses within $<5\%$ uncertainty, with efficiencies of $21\%$, and $16$-$18\%$, respectively. By considering these mass functions, we expect that the Roman telescope during its mission will detect and characterize $3$-$4$, $15$-$17$ and $22$-$24$ ISMBHs through astrometric microlensing, with the relative errors for all physical parameters less than $1,~5,~10\%$, respectively. Microlensing events owing to ISMBHs with a mass $\simeq 10$-$25 M_{\odot}$ and located close to the observer with $D_l \lesssim 0.5 D_s$ while the source is inside the Galactic disk can be characterized with least errors.