Differentiating small-scale subhalo distributions in CDM and WDM models using persistent homology

TL;DR

This paper introduces a novel topological data analysis method using persistent homology to distinguish small-scale dark matter structures in CDM and WDM models, revealing significant differences at specific scales.

Contribution

The study develops a new persistent homology-based approach to differentiate dark matter models using cosmological simulation data, highlighting scale-dependent structural differences.

Findings

Significant statistical differences between CDM and WDM structures (p ≤ 0.001).

Persistent homology detects differences at scales around 100 kpc.

CDM produces more unconnected halo clusters; WDM generates more loops.

Abstract

The spatial distribution of galaxies at sufficiently small scales will encode information about the identity of the dark matter. We develop a novel description of the halo distribution using persistent homology summaries, in which collections of points are decomposed into clusters, loops and voids. We apply these methods, together with a set of hypothesis tests, to dark matter haloes in MW-analog environment regions of the cold dark matter (CDM) and warm dark matter (WDM) Copernicus Complexio $N$-body cosmological simulations. The results of the hypothesis tests find statistically significant differences (p-values $\leq$ 0.001) between the CDM and WDM structures, and the functional summaries of persistence diagrams detect differences at scales that are distinct from the comparison spatial point process functional summaries considered (including the two-point correlation function). The differences between the models are driven most strongly at filtration scales $\sim100$~kpc, where CDM generates larger numbers of unconnected halo clusters while WDM instead generates loops. This study was conducted on dark matter haloes generally; future work will involve applying the same methods to realistic galaxy catalogues.