Chord distribution along a line in the local Universe

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.