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Astrometric satellite Gaia is expected to observe non-interacting black hole(BH) binaries with luminous companions (LCs) (hereafter BH-LC binaries), adifferent population from BH X-ray binaries previously discovered. Thedetectability of BH-LC binaries with Gaia might be dependent on binaryevolution models. We investigated the Gaia's detectability of BH-LC binariesformed through isolated binary evolution by means of binary populationsynthesis technique, and examined its dependence on single and binary starmodels: supernova models, common envelope (CE) ejection efficiency $\alpha$,and BH natal kick models. We estimated that $1.1$ -- $46$ BH-LC binaries can bedetected within five-year observation, and found that $\alpha$ has the largestimpacts on the detectable number. In each model, observable and intrinsic BH-LCbinaries have similar distributions. Therefore, we found three importantimplications: (1) if the lower BH mass gap is not intrinsic (i.e. $3$ -- $5M_\odot$ BHs exist), Gaia will observe $\leq 5 M_\odot$ BHs, (2) we may observeshort orbital period binaries with light LCs if CE efficiency is significantlyhigh, and (3) we may be able to identify the existence of natal kick fromeccentricity distribution.

Detectablity of Black Hole Binaries with Gaia: Dependence on Binary Evolution Models