A new hybrid technique for modeling dense star clusters

The “gravitational million-body problem,” to model the dynamical evolution of a self-gravitating, collisional N-body system with ～10⁶ particles over many relaxation times, remains a major challenge in computational astrophysics. Unfortunately, current techniques to model such systems suffer from severe limitations. A direct N-body simulation with more than 10⁵ particles can require months or even years to complete, while an orbit-sampling Monte Carlo approach cannot adequately model the dynamics in a dense cluster core, particularly in the presence of many black holes. We have developed a new technique combining the precision of a direct N-body integration with the speed of a Monte Carlo approach. Our Rapid And Precisely Integrated Dynamics code, the RAPID code, statistically models interactions between neighboring stars and stellar binaries while integrating directly the orbits of stars or black holes in the cluster core. This allows us to accurately simulate the dynamics of the black holes in a realistic globular cluster environment without the burdensome \(N^{2}\) scaling of a full N-body integration. We compare RAPID models of idealized globular clusters to identical models from the direct N-body and Monte Carlo methods. Our tests show that RAPID can reproduce the half-mass radii, core radii, black hole ejection rates, and binary properties of the direct N-body models far more accurately than a standard Monte Carlo integration while remaining significantly faster than a full N-body integration. With this technique, it will be possible to create more realistic models of Milky Way globular clusters with sufficient rapidity to explore the full parameter space of dense stellar clusters.