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

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.