Understanding the host galaxy properties of stellar binary black hole (SBBH) mergers is important for revealing the origin of the SBBH gravitational-wave sources detected by advanced LIGO and helpful for identifying their electromagnetic counterparts. Here we present a comprehensive analysis of the host galaxy properties of SBBHs by implementing semi-analytical recipes for SBBH formation and merger into cosmological galaxy formation model. If the time delay between SBBH formation and merger ranges from $la$,Gyr to the Hubble time, SBBH mergers at redshift $zla0.3$ occur preferentially in big galaxies with stellar mass $M_*ga2times10^{10}msun$ and metallicities $Z$ peaking at $sim0.6Z_odot$. However, the host galaxy stellar mass distribution of heavy SBBH mergers ($M_{bulletbullet}ga50msun$) is bimodal with one peak at $sim10^9msun$ and the other peak at $sim2times10^{10}msun$. The contribution fraction from host galaxies with $Zla0.2Z_odot$ to heavy mergers is much larger than that to less heavy mergers. If SBBHs were formed in the early universe (e.g., $z>6$), their mergers detected at $zla0.3$ occur preferentially in even more massive galaxies with $M_*>3times10^{10}msun$ and in galaxies with metallicities mostly $ga0.2Z_odot$ and peaking at $Zsim0.6Z_odot$, due to later cosmic assembly and enrichment of their host galaxies. SBBH mergers at $zla0.3$ mainly occur in spiral galaxies, but the fraction of SBBH mergers occur in elliptical galaxies can be significant if those SBBHs were formed in the early universe; and about two thirds of those mergers occur in the central galaxies of dark matter halos. We also present results on the host galaxy properties of SBBH mergers at higher redshift.
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