MYRIAD: a newN-body code for simulations of star clusters

Abstract

Aims. We present a new C++ code for collisional N-body simulations of star clusters. Methods. The code uses the Hermite fourth-order scheme with block time steps, to advance the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, and binary or multiple subsystems that form either dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions, and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6, could be replaced by another module that uses other accelerating-hardware such as the graphics processing units (GPUs).Results. Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. Simulations of Plummer models consisting of equal-mass stars reached core collapse at t 17 half-mass relaxation times, which compares very well with existing results, while the cumulative relative error in the energy remained below 10 −3 . Comparisons with published results of other codes for the time of core collapse for different initial conditions, show excellent agreement. Simulations of King models with an initial mass-function, similar to those found in the literature, reached core collapse at t 0.17 ± 0.05 half-mass relaxation times, which is slightly earlier than expected from previous work. Finally, the code accuracy becomes comparable to and even better than the accuracy of existing codes, when a number of close binary systems is dynamically created in a simulation. This is because of the high accuracy of the method that is used for close binary and multiple subsystems. Conclusions. The code can be used for evolving star clusters containing equal-mass stars or star clusters with an initial mass function (IMF) containing an intermediate mass black hole (IMBH) at the center and/or a fraction of primordial binaries, which are systems of particular astrophysical interest.

N-body integrators with individual time steps from Hierarchical splitting

“…In this case the core collapse occurs at t ≈ 350, and the evolution of the Lagrangian radii and core radius shows a pattern consistent with Giersz and Heggie (1994). The energy errors increase during the core collapse (for reference this can be compared with current Hermite codes in Konstantinidis and Kokkotas, 2010, their fig. 21).…”

“…The bin in which a particle resides determines the frequency of force evaluations and each successively higher bin has a factor 2 smaller interval between updates. This block time step scheme has been adopted in a wide range of codes, in for example codes for galactic simulations (Dubinski, 1996;Magorrian, 2007), cosmological simulations (Stadel, 2001), Smooth Particle Hydrodynamics codes (Springel, 2005;Wadsley et al, 2004) and also modern Hermite integrators for collisional stellar systems (Makino, 1991;Aarseth, 1999;Portegies Zwart et al, 2001;Harfst et al, 2008;Konstantinidis and Kokkotas, 2010). The popularity of this scheme stems from the fact that it allows for individual tailored time steps while still grouping particles with similar time steps together -which means that the cost of synchronizing the rest of the system is shared by all the particles in a given bin and parallelization of the force calculation is possible.…”

GraviDy: a modular, GPU-based, direct-summation N-body code

“…To numerically integrate the system of equations we adopt the widely known 4th-order Hermite integrator (H4 henceforth) presented in (Makino & Aarseth 1992; and see also Aarseth 1999Aarseth , 2003, which is a scheme based on a predictor-corrector scenario, in other words, the extrapolation and interpolation of the equations of motion. An advantage of the choice for H4 is that we can use the family of Aarseth's codes as a test for our implementation.…”

“…We are currently working on the implementation of a binary treatment which is based on the time-symmetric Hermite 4th order proposed by Kokubo et al (1998) and implemented by Konstantinidis & Kokkotas (2010). On the other hand, we are testing the adaptation of an Hermite 6th order scheme, as a alternative for the current 4th order.…”

A performance comparison of different graphics processing units running direct N-body simulations

“…"Direct summation" is the simplest to implement and the most accurate; nevertheless, its computational complexity is high (order of N 2 ), therefore it requires a huge computational power to be successfully applied to big (large N) astrophysical systems. The best known codes based on this approach are NBODY4, mainly developed by Sverre Aarseth [3] , φ-GRAPE [4], φ-GPU [5], the STARLAB environment [6], MYRIAD [7], NBSymple [8] and HiGPUs [9]. 2.…”