The Redshift Evolution of the Binary Black Hole Mass Distribution from Dense Star Clusters

Gravitational-wave detectors are unveiling a population of binary black hole (BBH) mergers out to redshifts $z \approx 1$, and are starting to constrain how the BBH population evolves with redshift. We present predictions for the redshift evolution of the BBH mass and spin distributions for systems originating from dense star clusters. Utilizing a grid of 144 state-of-the-art dynamical models for globular clusters, we demonstrate that BBH merger rates peak at higher redshifts for larger black hole primary masses $M_1$. Specifically, for $M_1\gtrsim40\,M_{\odot}$, the BBH merger rate reaches its peak at redshift $z\approx2.1$, while for $M_1\lesssim20\,M_{\odot}$, the peak occurs at $z\approx1.1$, assuming that the cluster formation rate peaks at $z=2.2$. The average BBH primary mass also increases from $\sim 10\,M_{\odot}$ at $z=0$ to $\sim 30\,M_{\odot}$ at $z=10$. We show that $\sim 20\%$ BBHs contain massive remnants from next-generation mergers, with this fraction increasing (decreasing) for larger (smaller) primary masses. This difference is not large enough to significantly alter the effective spins of the BBH population originating from globular clusters, and we find that their effective spin distribution does not evolve across cosmic time. These findings can be used to distinguish BBHs from dense star clusters by future gravitational wave observations.