Collisionless gravitational systems: discrete or not discrete? — that’s the question

A collisionless gravitational system, starting from a generic configuration, evolves towards a stationary state. In the limit N → infinity (continuum limit), this is accompanied by the development of indefinitely fine structures in phase-space. This continuum hypothesis is traditionally assumed to break only on time scales compared to the two-body relaxation time (~0.1 * N / ln N). In this talk, I will show the existence of a much shorter relaxation time scale [~0.1 * N^1/6], after which phase-space gets degraded, and finer structures are precluded. For stars in a galaxy [N ~ 10¹¹], this happens in a few dynamical times, solving the old problem of the fast relaxation of collisionless systems without the subjective effect of coarse-graining. On the other hand, this may restrict the capability of N-body simulations to reproduce fine structures expected for dark matter halos.