Understanding the progenitor formation galaxies of merging binary black holes

With nearly a hundred gravitational wave detections, the origin of black hole mergers has become a key question. Here, we focus on understanding the typical galactic environment in which binary black hole mergers arise. To this end, we synthesize progenitors of binary black hole mergers as a function of the redshift of progenitor formation, present-day formation galaxy mass, and progenitor stellar metallicity for $240$ star formation and binary evolution models. We provide guidelines to infer the formation galaxy properties and time of formation, highlighting the interplay between the star formation rate and the efficiency of forming merging binary black holes from binary stars, both of which strongly depend on metallicity. We find that across models, over 50% of BBH mergers have a progenitor metallicity of a few tenths of Solar metallicity, however, inferring formation galaxy properties strongly depends on both the binary evolution model and global metallicity evolution. The numerous, low-mass black holes ($\mathrm{\lesssim 15\,M_{\odot}}$) trace the bulk of the star formation in galaxies heavier than the Milky Way ($M_\mathrm{Gal}$ $\mathrm{\gtrsim 10^{10.5}\,M_{\odot}}$). In contrast, heavier BBH mergers typically stem from larger black holes forming in lower metallicity dwarf galaxies ($M_\mathrm{Gal}$ $\mathrm{\lesssim 10^{9}\,M_{\odot}}$). We find that the progenitors of detectable binary black holes tend to arise from dwarf galaxies at a lower formation redshift ($\lesssim \, 1$). We also produce a posterior probability of the progenitor environment for any detected gravitational wave signal. For the massive GW150914 merger, we show that it likely came from a very low metallicity ($Z$ $\mathrm{\lesssim}\,0.025\,\mathrm{Z_{\odot}}$) environment.