clusterBHBdynamics: A fast code for the evolution of tidally limited star clusters and their binary-black-hole mergers

The evolution of star clusters is driven by internal and external mechanisms, including stellar mass loss, two-body relaxation, and evaporation in the Galactic tidal field. Fast modelling tools are crucial for exploring diverse initial conditions and predicting cluster population properties and their contribution to gravitational wave (GW) sources over cosmic timescales. We present an improved version of the clusterBHBdynamics (̧bhbd) code, designed to evolve star clusters consisting of stars and stellar mass black holes (BHs). Regarding cluster evolution, we aim to improve the description of evaporation in the Galactic tidal field and add the effect of different metallicities and different stellar mass functions. For the GW part, we intend to add a new prescription for GW captures occurring in BBH--BBH interactions and for GW captures in between resonant interactions due to distant encounters that increase the eccentricity of the BBH. We validated the updated version of ̧bhbd against a suite of cluster Monte Carlo (̧mc) models for different initial cluster masses, radii, metallicities, and Galactic orbits. We also compared them to a suite of N-body simulations, and the GW predictions were compared to the BBH mergers in the ̧mc models and N-body simulations from the literature. Seven parameters of the ̧bhbd model are fitted to the ̧mc results with nested sampling. With the best-fit values, the evolution of the total cluster mass, half-mass radius, and the mass of the BH population over 13 are reproduced to within sim10%. With the new GW capture recipes, ̧bhbd now reproduces the BBH merger rate found in the ̧mc models of massive clusters (gtrsim10^5, and in direct N-body models of lower mass clusters (łesssim10^5, to within ∼ 20%. The improved ̧bhbd provides a fast and efficient tool for modelling cluster evolution, capturing essential dynamical effects while maintaining flexibility and scalability for large-scale star-cluster-population studies. With a typical runtime of one second per cluster, ̧bhbd enables iterative applications such as the search for initial conditions of globular clusters (GCs), the modelling of stellar streams, and GW population synthesis.