The Caustic Design of the Dark Matter Web

TL;DR

This paper introduces a novel method to directly identify and analyze caustic surfaces in dark matter simulations, revealing new geometrical features and surpassing previous resolution limitations.

Contribution

The authors develop a generic triangulation-based algorithm to reliably detect caustic surfaces in N-body simulations, improving resolution and revealing unexpected geometrical properties.

Findings

First reliable direct construction of caustic surfaces in simulations

Caustic shapes differ significantly from Zeldovich approximation predictions

Achieved resolution of caustic shells up to seven layers

Abstract

Matter density is formally infinite at the location of caustic surfaces, where dark matter sheet folds in phase-space. The caustics separate regions with different number of streams and the volume elements change the parity by turning inside out when passing through the caustic stage. Being measure-zero structures, identification of caustics via matter density fields is usually restricted to fine-grained simulations. Here we employ a generic algorithm to identify caustics directly using the triangulation of the Lagrangian sub-manifold x(q,t) obtained in N-body simulations. In our approach the caustic surfaces are approximated by a set of triangles whose vertices are particles of the simulation. The major obstacle we encountered was insufficient sampling of small scale perturbations. We overcame it by a brute force approach. We continued to raise the scale of the cutoff in the initial power spectrum until obtained the reliable resolution of the caustics shells up to seven layers. Although quite modest, our result is the first reliable direct construction of caustic surfaces in N-body simulation. It reveals a number of unexpected geometrical features. In particular shapes of some of them are contrastingly different from the known shapes of the caustics formed in the Zeldovich approximation.