tokens: placed in very dense environments near the Galactic center. The number of BH-LCs decreases with increasing natal kick magnitudes, as larger kicks disrupt a larger fraction of primordial binaries. For the same reason, natal kicks also affect the distribution of P orb of BH-LCs. While BH-LCs are disrupted in the Zero-kick model only if the change in mass during BH formation is severe enough to reduce the orbital binding energy to the point of unbinding, the NS-kick model leads to disruption of BH-LC progenitors with . We find a significant population of BH-LCs with P orb longer than the nominal Gaia mission in all of the models except the NS-kick model. This population exclusively contains BH-LCs that have not experienced a common envelope evolution. The population with orbital periods in the Gaia -observable range and lower contain BH-LCs that have experienced a common envelope, as well as BH-LCs that have not. Our NS-kick model does not allow formation of BH-LCs with and , while other models with lower natal kicks allow formation of these systems (Figure 2 ). By extending the Gaia mission beyond the nominal , our condition could be relaxed, and Gaia may constrain highly uncertain BH natal kicks from the properties of detected BH-LCs at longer orbital periods. 3.2. Gaia-observable Population Figure 3 shows the number of systems observable by Gaia () as a function of limiting G magnitude. The number of observable systems is inversely related to the BH natal kick strength because the likelihood of unbinding a BH-LC progenitor increases with kick strength. Figure 3. Mean number of observable BH-LCs as a function of limiting G magnitude computed from 500 Galactic realizations. Shades show regions above and below the mean denoted by the lines. Dashed (solid) lines denote our estimates using pessimistic (optimistic) astrometric cuts (Section 2.4 ). Blue, red, and black shading denote Zero-kick, FB-kick, and NS-kick models, respectively. Table 1 shows the result of our astrometric cuts. The total number of BH-LCs formed in our models is roughly consistent with the estimates in Mashian Loeb ( 2017 ). However, the majority of the systems formed lie above our upper cut (Figure 2 ). In addition to the natal kick prescription, the Galactic component has a noticeable effect on the number of BH-LC systems. Because the thick disk is modeled as a single star burst ago, all of the LCs in the thick disk at present are low mass. Large natal kicks for BHs such as our NS-kick model affect BH-LCs with low-mass LCs more (Figure 2 ; Section 3.1 ). As a result, in the thick disk, the NS-kick model yields a very low . The adopted continuous SFR in the thin disk keeps relatively high even for the NS-kick model by forming high-mass luminous stars very close to the present epoch. Table 1 Average Number of BH-LCs Observable by Gaia from 500 Galactic Realizations with for Our Optimistic and Pessimistic Cuts (Section 2.4 ) We estimate 3800–12,000 BH-LCs in the MW are
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