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Understanding the host galaxy properties of stellar binary black hole (SBBH)mergers is important for revealing the origin of the SBBH gravitational-wavesources detected by advanced LIGO and helpful for identifying theirelectromagnetic counterparts. Here we present a comprehensive analysis of thehost galaxy properties of SBBHs by implementing semi-analytical recipes forSBBH formation and merger into cosmological galaxy formation model. If the timedelay between SBBH formation and merger ranges from $\la$\,Gyr to the Hubbletime, SBBH mergers at redshift $z\la0.3$ occur preferentially in big galaxieswith stellar mass $M_*\ga2\times10^{10}\msun$ and metallicities $Z$ peaking at$\sim0.6Z_\odot$. However, the host galaxy stellar mass distribution of heavySBBH mergers ($M_{\bullet\bullet}\ga50\msun$) is bimodal with one peak at$\sim10^9\msun$ and the other peak at $\sim2\times10^{10}\msun$. Thecontribution fraction from host galaxies with $Z\la0.2Z_\odot$ to heavy mergersis much larger than that to less heavy mergers. If SBBHs were formed in theearly universe (e.g., $z>6$), their mergers detected at $z\la0.3$ occurpreferentially in even more massive galaxies with $M_*>3\times10^{10}\msun$ andin galaxies with metallicities mostly $\ga0.2Z_\odot$ and peaking at$Z\sim0.6Z_\odot$, due to later cosmic assembly and enrichment of their hostgalaxies. SBBH mergers at $z\la0.3$ mainly occur in spiral galaxies, but thefraction of SBBH mergers occur in elliptical galaxies can be significant ifthose SBBHs were formed in the early universe; and about two thirds of thosemergers occur in the central galaxies of dark matter halos. We also presentresults on the host galaxy properties of SBBH mergers at higher redshift.

Host galaxy properties of mergers of stellar binary black holes and their implications for advanced LIGO gravitational wave sources