Binary black hole mergers from globular clusters: Masses, merger rates, and the impact of stellar evolution

The recent discovery of GW150914, the binary black hole merger detected by Advanced LIGO, has the potential to revolutionize observational astrophysics. But to fully utilize this new window into the Universe, we must compare these new observations to detailed models of binary black hole formation throughout cosmic time. Expanding upon our previous work [C. L. Rodriguez, M. Morscher, B. Pattabiraman, S. Chatterjee, C.-J. Haster, and F. A. Rasio, Phys. Rev. Lett. 115, 051101 (2015).], we study merging binary black holes formed in globular clusters using our Monte Carlo approach to stellar dynamics. We have created a new set of 52 cluster models with different masses, metallicities, and radii to fully characterize the binary black hole merger rate. These models include all the relevant dynamical processes (such as two-body relaxation, strong encounters, and three-body binary formation) and agree well with detailed direct $N$-body simulations. In addition, we have enhanced our stellar evolution algorithms with updated metallicity-dependent stellar wind and supernova prescriptions, allowing us to compare our results directly to the most recent population synthesis predictions for merger rates from isolated binary evolution. We explore the relationship between a cluster's global properties and the population of binary black holes that it produces. In particular, we derive a numerically calibrated relationship between the merger times of ejected black hole binaries and a cluster's mass and radius. With our improved treatment of stellar evolution, we find that globular clusters can produce a significant population of massive black hole binaries that merge in the local Universe. We explore the masses and mass ratios of these binaries as a function of redshift, and find a merger rate of $\ensuremath{\sim}5\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}{\mathrm{yr}}^{\ensuremath{-}1}$ in the local Universe, with 80% of sources having total masses from $32{M}_{\ensuremath{\bigodot}}$ to $64{M}_{\ensuremath{\bigodot}}$. Under standard assumptions, approximately one out of every seven binary black hole mergers in the local Universe will have originated in a globular cluster, but we also explore the sensitivity of this result to different assumptions for binary stellar evolution. If black holes were born with significant natal kicks, comparable to those of neutron stars, then the merger rate of binary black holes from globular clusters would be comparable to that from the field, with approximately $1/2$ of mergers originating in clusters. Finally we point out that population synthesis results for the field may also be modified by dynamical interactions of binaries taking place in dense star clusters which, unlike globular clusters, dissolved before the present day.