Introducing a new multi-particle collision method for the evolution of dense stellar systems

Abstract

Context. Stellar systems are broadly divided into collisional and non-collisional categories. While the latter are large-N systems with long relaxation timescales and can be simulated disregarding two-body interactions, either computationally expensive direct N-body simulations or approximate schemes are required to properly model the former. Large globular clusters and nuclear star clusters, with relaxation timescales of the order of a Hubble time, are small enough to display some collisional behaviour and big enough to be impossible to simulate with direct N-body codes and current hardware. Aims. We aim to introduce a new method to simulate collisional stellar systems and validate it by comparison with direct N-body codes on small-N simulations. Methods. The Multi-Particle Collision for Dense Stellar Systems (MPCDSS) code is a new code for evolving stellar systems with the multi-particle collision method. Such a method amounts to a stochastic collision rule that makes it possible to conserve the exact energy and momentum over a cluster of particles experiencing the collision. The code complexity scales with N log N in the number of particles. Unlike Monte Carlo codes, MPCDSS can easily model asymmetric, non-homogeneous, unrelaxed, and rotating systems, while allowing us to follow the orbits of individual stars. Results. We evolved small (N = 3.2 × 104) star clusters with MPCDSS and with the direct-summation code NBODY6, finding a similar evolution of key indicators. We then simulated different initial conditions in the 104 − 106 star range. Conclusions. MPCDSS bridges the gap between small collisional systems that can be simulated with direct N-body codes and large non-collisional systems. In principle, MPCDSS allows us to simulate globular clusters such as Ω Centauri and M 54, and even nuclear star clusters, which is beyond the limits of current direct N-body codes in terms of the number of particles.