Exploring the non-linear density field in the millennium simulations with tessellations - I. the probability distribution function

Abstract

We use the Delaunay Tessellation Field Estimator (DTFE) to study the one-point density distribution functions of the Millennium Simulation (MS) and Millennium-II Simulation (MS-II). The DTFE technique is based directly on the particle positions, without requiring any type of smoothing or analysis grid, thereby providing high sensitivity to all non-linear structures resolved by the simulations. In order to identify the detailed origin of the shape of the onepoint density probability distribution function (PDF), we decompose the simulation particles according to the mass of their host FoF haloes, and examine the contributions of different halo mass ranges to the global density PDF. We model the one-point distribution of the FoF haloes in each halomass bin with a set of Monte Carlo realizations of idealized Navarro-Frenk-White (NFW) dark matter haloes, finding that this reproduces the measurements from the N-body simulations reasonably well, except for a small excess present in simulation results. This excess increases with increasing halo mass. We show that its origin lies in substructure, which becomes progressively more abundant and better resolved in more massive dark matter haloes. We demonstrate that the high-density tail of the one-point distribution function in less massive haloes is severely affected by the gravitational softening length and the mass resolution. In particular, we find these two parameters to be more important for an accurate measurement of the density PDF than the simulated volume. Combining our results from individual halo mass bins we find that the part of the one-point density PDF originating from collapsed haloes can nevertheless be quite well described by a simple superposition of a set of NFW haloes with the expected cosmological abundance over the resolved mass range. The transition region to the low-density unbound material is however not well captured by such an analytic halo model. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.