Metallicity dependence of black hole main sequence binaries detectable with Gaia

LIGO has detected gravitational waves from massive binary black hole mergers. In order to explain the origin of such massive stellar-mass black holes, extreme metal poor stars including first stars have been invoked. However, black holes do not carry information of the metallicity. In order to check the metallicity dependence of the black hole formation, we focus on galactic black hole-main sequence binaries (BH-MSs). Using a binary population synthesis method, we find that $gaia$ can detect $sim200-400$ BH-MSs whose metallicity is $zsun$ and $sim70-400$ BH-MSs whose metallicity is $0.1zsun$. With the spectroscopic observation on 4-m class telescopes, we can check the metallicity of BH-MSs. The metallicity dependence of the black hole formation might be checked by the astrometry and spectroscopic observations.