VlasovPoisson in 1D: waterbags
Abstract
We revisit in one dimension the waterbag method to solve numerically VlasovPoisson equations. In this approach, the phasespace distribution function f (x, v) is initially sampled by an ensemble of patches, the waterbags, where f is assumed to be constant. As a consequence of Liouville theorem, it is only needed to follow the evolution of the border of these waterbags, which can be done by employing an orientated, selfadaptive polygon tracing isocontours of f. This method, which is entropy conserving in essence, is very accurate and can trace very well nonlinear instabilities as illustrated by specific examples. As an application of the method, we generate an ensemble of singlewaterbag simulations with decreasing thickness to perform a convergence study to the cold case. Our measurements show that the system relaxes to a steady state where the gravitational potential profile is a power law of slowly varying index β, with β close to 3/2 as found in the literature. However, detailed analysis of the properties of the gravitational potential shows that at the centre, β > 1.54. Moreover, our measurements are consistent with the value β = 8/5 = 1.6 that can be analytically derived by assuming that the average of the phasespace density per energy level obtained at crossing times is conserved during the mixing phase. These results are incompatible with the logarithmic slope of the projected density profile β  2 ≃ 0.47 obtained recently by Schulz et al. using an Nbody technique. This sheds again strong doubts on the capability of Nbody techniques to converge to the correct steady state expected in the continuous limit.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 July 2014
 DOI:
 10.1093/mnras/stu739
 Bibcode:
 2014MNRAS.441.2414C
 Keywords:

 gravitation;
 methods: numerical;
 galaxies: kinematics and dynamics;
 dark matter