The Tessellation-Level-Tree: characterising the nested hierarchy of density peaks and their spatial distribution in cosmological N-body simulations

We use the Millennium and Millennium-II simulations to illustrate the Tessellation-Level-Tree (TLT), a hierarchical tree structure linking density peaks in a field constructed by voronoi tessellation of the particles in a cosmological N-body simulation. The TLT uniquely partitions the simulation particles into disjoint subsets, each associated with a local density peak. Each peak is a subpeak of a unique higher peak. The TLT can be persistence filtered to suppress peaks produced by discreteness noise. Thresholding a peak's particle list at $\sim 80\left<ρ\right>$ results in a structure similar to a standard friend-of-friends halo and its subhaloes. For thresholds below $\sim 7\left<ρ\right>$, the largest structure percolates and is much more massive than other objects. It may be considered as defining the cosmic web. For a threshold of $5\left<ρ\right>$, it contains about half of all cosmic mass and occupies $\sim 1\%$ of all cosmic volume; a typical external point is then $\sim 7h^{-1}\mathrm{Mpc}$ from the web. We investigate the internal structure and clustering of TLT peaks. Defining the saddle point density $ρ_{\mathrm{lim}}$ as the density at which a peak joins its parent peak, we show the median value of $ρ_{\mathrm{lim}}$ for FoF-like peaks to be similar to the density threshold at percolation. Assembly bias as a function of $ρ_{\mathrm{lim}}$ is stronger than for any known internal halo property. For peaks of group mass and below, the lowest quintile in $ρ_{\mathrm{lim}}$ has $b\approx 0$, and is thus uncorrelated with the mass distribution.

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