**Title**: Particle number dependence in the non-linear evolution of N-body

self-gravitating systems

**Authors**: David Benhaiem, Michael Joyce, Francesco Sylos Labini and Tirawut

Worrakitpoonpon

**Categories**: astro-ph.CO

**Comments**: 8 pages, 5 figures; to appear in MNRAS

**License**: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

https://arxiv.org/abs/1709.06657

Simulations of purely self-gravitating N-body systems are often used in

astrophysics and cosmology to study the collisionless limit of such systems.

Their results for macroscopic quantities should then converge well for

sufficiently large N. Using a study of the evolution from a simple space of

spherical initial conditions – including a region characterised by so-called

“radial orbit instability” – we illustrate that the values of N at which such

convergence is obtained can vary enormously. In the family of initial

conditions we study, good convergence can be obtained up to a few dynamical

times with N $ \sim 10^3$ – just large enough to suppress two body relaxation –

for certain initial conditions, while in other cases such convergence is not

attained at this time even in our largest simulations with N $\sim 10^5$. The

qualitative difference is due to the stability properties of fluctuations

introduced by the N-body discretisation, of which the initial amplitude depends

on N. We discuss briefly why the crucial role which such fluctuations can

potentially play in the evolution of the N-body system could, in particular,

constitute a serious problem in cosmological simulations of dark matter.