Stochasticity in N-body simulations of disc galaxies

We demonstrate that the chaotic nature of N-body systems can lead to macroscopic variations in the evolution of collisionless simulations containing rotationally supported discs. The unavoidable stochasticity that afflicts all simulations generally causes mild differences between the evolution of similar models but, in order to illustrate that this is not always true, we present a case that shows an extreme bimodal divergence. The divergent behaviour occurs in two different types of code, and is independent of all numerical parameters. We identify and give explicit illustrations of several sources of stochasticity, and also show that macroscopic variations in the evolution can originate from differences at the round-off error level. We obtain somewhat more consistent results from simulations in which the halo is set-up with great care compared with those started from more approximate equilibria, but we have been unable to eliminate diverging behaviour entirely because the main sources of stochasticity are intrinsic to the disc. We show that the divergence is only temporary and that halo friction is merely delayed, for a substantial time in some cases. We argue that the delays are unlikely to arise in real galaxies, and that our results do not affect dynamical friction constraints on halo density. Stochastic variations in the evolution are inevitable in all simulations of disc-halo systems, irrespective of how they were created, although their effect is generally far less extreme than we find here. The possibility of divergent behaviour complicates comparison of results from different workers.