$N$-body chaos, phase-space transport and relaxation in numerical simulations

Abstract

Using direct $N$-body simulations of self-gravitating systems we study the dependence of dynamical chaos on the system size $N$. We find that the $N$-body chaos quantified in terms of the largest Lyapunov exponent ${\Lambda }_{\max }$ decreases with $N$. The values of its inverse (the so-called Lyapunov time $t_{\lambda }$) are found to be smaller than the two-body collisional relaxation time but larger than the typical violent relaxation time, thus suggesting the existence of another collective time scale connected to many-body chaos.

4 pages, 2 figures. To appear in the proceedings of the 351 IAU Symposium "Star Clusters: from the Milky Way to the Early Universe"