Geometry of the Cosmic Web: Minkowski Functionals from the Delaunay Tessellation

TL;DR

This paper introduces a new method to compute Minkowski Functionals directly from Delaunay tessellations, improving the analysis of complex, nonuniform cosmic structures like galaxy superclusters and voids.

Contribution

The novel approach allows for more accurate geometric analysis of nonuniform density fields in cosmology, overcoming limitations of previous grid-based methods.

Findings

Successfully tested on geometric models

Applied to N-body simulation data

Demonstrated improved geometric analysis capabilities

Abstract

We present a novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological studies when the isodensity surface was built in the field on a uniform cubic grid and therefore having a uniform spatial resolution. The density field representing a particular interest in cosmology is the density of galaxies which is obtained from the highly nonuniform distribution of the galaxy positions. Therefore, the constraints caused by the spatially uniform grid put severe limitations on the studies of the geometry and shapes of the large-scale objects: superclusters and voids of galaxies. Our technique potentially is able to eliminate most of these limitations. The method is tested with some simple geometric models and an application to the density field from an N-body simulation is shown.