Influence of Black Hole Kick Velocity on Microlensing Distributions

The natal kick velocity distribution for black holes (BHs) is unknown regardless of its importance for understanding the BH formation process. Gravitational microlensing is a unique tool for studying the distribution of BHs in our Galaxy, and the first isolated stellar-mass BH event, OGLE-2011-BLG-0462/MOA-2011-BLG-191 (OB110462), was recently identified by astrometric microlensing. This study investigates how the natal kick velocity for Galactic BHs affects the microlensing event rate distribution. We consider a Maxwell distribution with various average kick velocities, as well as the consequent variation of the spatial distribution of BHs. We find that the event rate for the BH lenses toward the Galactic bulge decreases as $v_{\rm avg}$ increases, mainly due to the scale height inflation. We focus on the unique microlensing parameters measured for OB110462, with microlens parallax $\pi_{\rm E}$ larger than 0.06 for its long timescale of $t_{\rm E} > 200~$ days. We calculate the expected number of BH events occurring with parameters similar to OB110462 during the OGLE-IV survey by Mr\'oz et al. (2017, 2019) and compare it with the actual number that occurred, at least one. Our fiducial model predicts 0.26, 0.19, 0.095, 0.020, and $1.8 \times 10^{-3}$ events occurring for $v_{\rm avg} =$ 25 km/sec, 50 km/sec, 100 km/sec, 200 km/sec, and 400 km/sec, respectively, which suggests that the average kick velocity is likely to be $v_{\rm avg} \lesssim 100~{\rm km/sec}$. The expected number smaller than unity even at maximum might indicate our luckiness of finding OB110462, which can be tested with future surveys by e.g. the Roman space telescope.