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Vlasov versus N-body: the Hénon sphere

Abstract : 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, R ≃ 0.1 and 0.5. After checking that spherical symmetry is well preserved by the N-body simulations, visual and quantitative comparisons are performed. In particular, we introduce new statistics, correlators and entropic estimators, based on the likelihood of whether N-body simulations actually trace randomly the Vlasov phase-space density. When taking into account the limits of both the N-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, R = 0.1, it was not possible to prove actual numerical convergence of the N-body results after a number of dynamical times, even with N = 108 particles.
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S. Colombi, T. Sousbie, S. Peirani, G. Plum, y. Suto. Vlasov versus N-body: the Hénon sphere. Monthly Notices of the Royal Astronomical Society, Oxford University Press (OUP): Policy P - Oxford Open Option A, 2015, 450, pp.3724-3741. ⟨10.1093/mnras/stv819⟩. ⟨insu-03644901⟩

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