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

TL;DR

This paper introduces the Tessellation-Level-Tree (TLT), a hierarchical structure that characterizes the nested density peaks and their spatial distribution in cosmological N-body simulations, revealing insights into cosmic web formation.

Contribution

The TLT provides a novel hierarchical framework for analyzing density peaks and their relationships, enhancing understanding of cosmic web structure and halo formation in simulations.

Findings

TLT effectively partitions particles into density peaks and subpeaks.

Percolation threshold at low density captures the cosmic web.

Assembly bias varies with saddle point density, affecting clustering.

Abstract

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 $\sim 80\left<\rho\right>$ results in a structure similar to a standard friend-of-friends halo and its subhaloes. For thresholds below $\sim 7\left<\rho\right>$, 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 $5\left<\rho\right>$, 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 $\rho_{\mathrm{lim}}$ as the density at which a peak joins its parent peak, we show the median value of $\rho_{\mathrm{lim}}$ for FoF-like peaks to be similar to the density threshold at percolation. Assembly bias as a function of $\rho_{\mathrm{lim}}$ is stronger than for any known internal halo property. For peaks of group mass and below, the lowest quintile in $\rho_{\mathrm{lim}}$ has $b\approx 0$, and is thus uncorrelated with the mass distribution.