Modeling the evolution of binary black hole mergers in dense stellar environments

Binary black hole (BBH) mergers are critical sources of gravitational waves detected by observatories like LIGO and Virgo. The formation and evolution of these binaries, particularly in dense stellar environments such as globular clusters (GCs) and galactic nuclei, are crucial for understanding the observed BBH population. In this study, we develop a Monte Carlo N-body simulation model to simulate the dynamical evolution of BBH mergers in such environments. We incorporate key processes, including two-body relaxation, three-body encounters, exchange interactions, and gravitational wave emission. Our results indicate that globular clusters can produce BBH merger rates of approximately 20 mergers per Gyr per 105M☉, in agreement with current gravitational wave observations. The simulated mass distribution of BBHs peaks at around 20 M ☉, with a tail extending to 50 M ☉, and the spin orientations are predominantly isotropic. These findings highlight the significant role dense stellar environments play in the formation of BBHs. We also discuss the uncertainties in the model and suggest future work to refine the simulations and better constrain the contribution of dense stellar environments to the overall BBH merger rate.