Introducing a new multi-particle collision method for the evolution of dense stellar systems. Crash-test N-body simulations (original) (raw)
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Introducing a new multi-particle collision method for the evolution of dense stellar systems
Astronomy and Astrophysics, 2021
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.
2020
Stellar systems are broadly divided into collisional and non-collisional. The latter are large-N systems with long relaxation timescales and can be simulated disregarding two-body interactions, while 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 NNN-body codes and current hardware. We introduce a new method to simulate collisional stellar systems, and validate it by comparison with direct N-body codes on small-N simulations. The Multi-Particle collision for Dense stellar systems Code (MPCDSS) is a new code for evolving stellar systems with the Multi-Particle Collision method. Such method amounts to a stochastic collision rule that allows to conserve exactly the energy and momentum over a c...
2021
In a previous paper we introduced a new method for simulating collisional gravitational N-body systems with linear time scaling on N, based on the Multi-Particle Collision (MPC) approach. This allows us to simulate globular clusters with a realistic number of stellar particles in a matter of hours on a typical workstation. We evolve star clusters containing up to 10^6 stars to core collapse and beyond. We quantify several aspects of core collapse over multiple realizations and different parameters, while always resolving the cluster core with a realistic number of particles. We run a large set of N-body simulations with our new code. The cluster mass function is a power-law with no stellar evolution, allowing us to clearly measure the effects of the mass spectrum. Leading up to core collapse, we find a power-law relation between the size of the core and the time left to core collapse. Our simulations thus confirm the theoretical self-similar contraction picture but with a dependence...
2012
In this thesis we study several aspects of dynamical evolution of stellar clusters. The results of more than 200 simulations of single-mass star clusters with different initial total mass, half-mass radius and galactocentric distance, are reported. Recent studies of star clusters show a linear relation between a star cluster's dissolution time and its two-body relaxation time in logarithmic scale. We found that the single-mass star clusters do not show such a linear relation. We present new modified initial parameters to obtain a linear relation for single-mass star clusters. Also the evolution of multi-mass clusters and their lifetime, in the presence of the Galaxy is investigated. We simulate about 90 multi-mass star clusters with the Nbody6 code. These clusters have different initial total mass, half-mass radius and galactocentric distance. Finally we investigate the evolution of the stellar mass function and show that the slopes of the mass functions decrease with time. In a...
Monthly Notices of the Royal Astronomical Society, 2003
Spherically symmetric equal mass star clusters containing a large amount of primordial binaries are studied using a hybrid method, consisting of a gas dynamical model for single stars and a Monte Carlo treatment for relaxation of binaries and the setup of close resonant and fly-by encounters of single stars with binaries and binaries with each other (three-and four-body encounters). What differs from our previous work is that each encounter is being integrated using a highly accurate direct few-body integrator which uses regularized variables. Hence we can study the systematic evolution of individual binary orbital parameters (eccentricity, semi-major axis) and differential and total cross sections for hardening, dissolution or merging of binaries (minimum distance) from a sampling of several ten thousands of scattering events as they occur in real cluster evolution including mass segregation of binaries, gravothermal collapse and reexpansion, binary burning phase and ultimately gravothermal oscillations. For the first time we are able to present empirical cross sections for eccentricity variation of binaries in close three-and four-body encounters. It is found that a large fraction of three-body and four-body encounters results in merging. Eccentricities are generally increased in strong three-and four-body encounters and there is a characteristic scaling law ∝ exp(4e fin ) of the differential cross section for eccentricity changes, where e fin is the final eccentricity of the binary, or harder binary for four-body encounters. Despite of these findings the overall eccentricity distribution remains thermal for all binding energies of binaries, which is understood from the dominant influence of resonant encounters. Previous cross sections obtained by Spitzer and Gao for strong encounters can be reproduced, while for weak encounters non-standard processes like formation of hierarchical triples occur.
Cosmological N-Body Simulations
Computers in Physics, 1991
In this review we discuss Cosmological N-Body codes with a special emphasis on Particle Mesh codes. We present the mathematical model for each component of N-Body codes. We compare alternative methods for computing each quantity by calculating errors for each of the components. We suggest an optimum set of components that can be combined reduce overall errors in N-Body codes.
Tools and Techniques for N-body Simulations
Memorie della Societa Astronomica Italiana Supplementi, 2003
Computational Astrophysics research often requires very powerful machines, and very sophisticated codes. In stellar dynamics simulations, the development of the treecode, and the realisation of the GRAPE special purpose device, have contributed dramatically to the progress of scientific research. The pseudoparticle approach, where a multipole expansion is expressed in terms of a particle distribution, allows to improve the tree-code accuracy at a limited computational cost. Moreover, it is suitable for making full use of the GRAPE. We study the error behaviour of this approach with respect to changing physical distributions. Thus we introduce improvements that reduce the errors. Furthermore we present an extension of the pseudo-particle scheme, where pseudo-particles are not fixed in space, but move following the physical particle distribution. This extension decreases the computational overhead due to pseudo-particle recomputation, and optimises the scheme for the use on GRAPE and on parallel systems. We also study the efficiency at which a black hole spirals-in to the Galactic centre, using the direct N-body method running on the GRAPE, a tree algorithm and a particle-mesh technique. The three different techniques are in excellent agreement. The black hole infall, within the set of parameters that we consider, is not influenced by the granularity of the N-body system.
N ‐Body Simulations of Compact Young Clusters near the Galactic Center
The Astrophysical Journal, 2000
We investigate the dynamical evolution of compact young star clusters (CYCs) near the Galactic center (GC) using Aarseth's Nbody6 codes. The relatively small number of stars in the cluster (5,000-20,000) makes real-number N-body simulations for these clusters feasible on current workstations. Using Fokker-Planck (F-P) models, Kim, Morris, & Lee (1999) have made a survey of cluster lifetimes for various initial conditions, and have found that clusters with a mass ∼ < 2 × 10 4 M ⊙ evaporate in ∼ 10 Myr. These results were, however, to be confirmed by N-body simulations because some extreme cluster conditions, such as strong tidal forces and a large stellar mass range participating in the dynamical evolution, might violate assumptions made in F-P models. Here we find that, in most cases, the CYC lifetimes of previous F-P calculations are 5-30 % shorter than those from the present N-body simulations. The comparison of projected number density profiles and stellar mass functions between N-body simulations and HST/NICMOS observations by Figer et al. (1999) suggests that the current tidal radius of the Arches cluster is ∼ 1.0 pc, and the following parameters for the initial conditions of that cluster: total mass of 2 × 10 4 M ⊙ and mass function slope for intermediate-to-massive stars of 1.75 (the Salpeter function has 2.35). We also find that the lower stellar mass limit, the presence of primordial binaries, the amount of initial mass segregation, and the choice of initial density profile (King or Plummer models) do not significantly affect the dynamical evolution of CYCs.
NBODY6++GPU: ready for the gravitational million-body problem
Monthly Notices of the Royal Astronomical Society, 2015
Accurate direct N -body simulations help to obtain detailed information about the dynamical evolution of star clusters. They also enable comparisons with analytical models and Fokker-Planck or Monte-Carlo methods. NBODY6 is a well-known direct N -body code for star clusters, and NBODY6++ is the extended version designed for large particle number simulations by supercomputers. We present NBODY6++GPU, an optimized version of NBODY6++ with hybrid parallelization methods (MPI, GPU, OpenMP, and AVX/SSE) to accelerate large direct N -body simulations, and in particular to solve the million-body problem. We discuss the new features of the NBODY6++GPU code, benchmarks, as well as the first results from a simulation of a realistic c -RAS 2 L. Wang et al. globular cluster initially containing a million particles. For million-body simulations, NBODY6++GPU is 400 − 2000 times faster than NBODY6 with 320 CPU cores and 32 NVIDIA K20X GPUs. With this computing cluster specification, the simulations of million-body globular clusters including 5% primordial binaries require about an hour per half-mass crossing time. Direct simulations of star clusters have a long history. As algorithms and hardware have improved, larger numbers of stars could be simulated, allowing a more realistic representation of the dynamical evolution of globular star clusters. NBODY6 (Aarseth 2003) is a state-ofthe-art direct N-body simulation code specifically designed for star clusters. It uses several algorithms to enhance the computing speed and accuracy, especially for strong interactions that arise from a large fraction of binaries and relatively short relaxation timescales (≤ 100
Direct N-body simulations of globular clusters - II. Palomar 4
Monthly Notices of the Royal Astronomical Society, 2014
We present the first ever direct N -body computations of an old Milky Way globular cluster over its entire life time on a star-by-star basis. Using recent GPU hardware at Bonn University, we have performed a comprehensive set of N -body calculations to model the distant outer halo globular cluster Palomar 14 (Pal 14). Pal 14 is unusual in that its mean density is about ten times smaller than that in the solar neighborhood. Its large radius as well as its low-mass make it possible to simulate Pal 14 on a star-bystar basis. By varying the initial conditions we aim at finding an initial N -body model which reproduces the observational data best in terms of its basic parameters, i.e. half-light radius, mass and velocity dispersion. We furthermore focus on reproducing the stellar mass function slope of Pal 14 which was found to be significantly shallower than in most globular clusters.