Chord distribution along a line in the local Universe

TL;DR

This paper develops analytical formulas for chord length distributions in cellular models of the Universe, using Voronoi tessellations, and applies them to real and simulated galaxy survey data.

Contribution

It introduces new analytical formulas for chord distributions in both Poissonian and non-Poissonian Voronoi models of the Universe.

Findings

Formulas for chord length distributions in PVT and NPVT models.

Application to real galaxy survey data and simulations.

Enhanced understanding of large-scale cosmic structure geometry.

Abstract

A method is developed to compute the chord length distribution along a line which intersects a cellular Universe. The cellular Universe is here modeled by the Poissonian Voronoi Tessellation (PVT) and by a non-Poissonian Voronoi Tessellation (NPVT). The distribution of the spheres is obtained from common approximations used in modeling the volumes of Voronoi Diagrams. We give analytical formulas for the distributions of the lengths of chords in both the PVT and NPVT. The astrophysical applications are made to the real Eso Slice Project and to an artificial slice of galaxies which simulates the 2dF Galaxy Redshift Survey.