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