The Star Clusters That Make Black Hole Binaries across Cosmic Time

We explore the properties of dense star clusters that are likely to be nurseries of stellar black holes pairing in close binaries. We combine a cosmological model of globular cluster formation with analytic prescriptions for the dynamical assembly and evolution of black hole binaries (BHBs) to constrain which types of clusters are most likely to form binaries tight enough to coalesce within a Hubble time. We find that BHBs that are ejected and later merge ex situ form in clusters of a characteristic mass M-cl similar to 10(5.3) M-circle dot, whereas binaries that merge in situ form in more massive clusters, M-cl similar to 10(5.7) M-circle dot. The clusters that dominate the production of BHBs are similar in age and metallicity to the entire population. Finally, we estimate an approximate cosmic black hole merger rate of dynamically assembled binaries using the mean black hole mass for each cluster, given its metallicity. We find an intrinsic rate of similar to 6 Gpc(-3) yr(-1) at z = 0, a weakly increasing merger rate out to z = 1.5, and then a decrease out to z = 4. Our results can be used to provide a cosmological context and choose initial conditions in numerical studies of BHBs assembled in star clusters.