Vlasov versus N-body: the Hénon sphere

We perform a detailed comparison of the phase-space density traced by the particle distribution in gadget simulations to the result obtained with a spherical Vlasov solver using the splitting algorithm. The systems considered are apodized Hénon spheres with two values of the virial ratio, <it>R</it> ≃ 0.1 and 0.5. After checking that spherical symmetry is well preserved by the <it>N</it>-body simulations, visual and quantitative comparisons are performed. In particular, we introduce new statistics, correlators and entropic estimators, based on the likelihood of whether <it>N</it>-body simulations actually trace randomly the Vlasov phase-space density. When taking into account the limits of both the <it>N</it>-body and the Vlasov codes, namely collective effects due to the particle shot noise in the first case and diffusion and possible non-linear instabilities due to finite resolution of the phase-space grid in the second case, we find a spectacular agreement between both methods, even in regions of phase-space where non-trivial physical instabilities develop. However, in the colder case, <it>R</it> = 0.1, it was not possible to prove actual numerical convergence of the <it>N</it>-body results after a number of dynamical times, even with <it>N</it> = 108 particles.