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 × 10 4) 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 10 4 − 10 6 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 Omega Centauri and M54, and even nuclear star clusters, which is beyond the limits of current direct N-body codes in terms of the number of particles.

Lock-key microfluidics: simulating nematic colloid advection along wavy-walled channels

“…[39][40][41][42] MPCD has been employed to simulate reactiondiffusion dynamics, 43,44 electrophoresis, 45,46 thermophoresis, 47 swimmers, [48][49][50] polymers, [51][52][53][54] colloidal suspensions, 55,56 binary mixtures, 57 viscoelastic fluids, 58 ferrofluids, 59,60 and dense stellar systems. [61][62][63] Most relevantly, MPCD has been used to simulate nematic liquid crystals. 64 In this context, MPCD has simulated nematohydrodynamics, 65 suspended colloids, 66,67 magnetic colloids, 68,69 living liquid crystals, 70 and active nematics.…”

Symplectic coarse graining approach to the dynamics of spherical self-gravitating systems

“…In order to speed up the calculations and enforce the preservation of the spherical symmetry, we solve only the radial part of Eq. ( 49), averaging out the contributions in ϑ and ϕ, similarly to what was done in Pattabiraman et al (2013); Rodriguez et al (2018); Di Cintio et al (2021). By doing so, in practice, the particles' equations of motion become ri = − GM (ri)…”

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

“…Alternatives to direct N-body simulations are approximate methods, typically based on solving the Fokker-Planck equation (e.g., , for a state-of-the-art Monte Carlo solver), resulting in dramatically shorter run times. In a previous paper (Di Cintio et al 2021 we introduced a code for simulating gravitational N-body systems, called MPCDSS, that takes a new approach to approximating collisional evolution through the so-called multi-particle collision (MPC) method. We refer the reader to D2020 for details on the method, its rationale, and its implementation.…”