Practical Statistics for the Voids Between Galaxies

TL;DR

This paper models cosmic voids between galaxies using Poisson Voronoi tessellations, deriving new survival functions for void radii and simulating their appearance in galaxy survey slices.

Contribution

It introduces novel survival functions for void radii based on Poisson Voronoi tessellations and models the sectional area distribution with Kiang and exponential functions.

Findings

Derived new survival functions for void radii.

Modeled sectional area distribution with Kiang and exponential functions.

Simulated galaxy survey slices showing void structures.

Abstract

The voids between galaxies are identified with the volumes of the Poisson Voronoi tessellation. Two new survival functions for the apparent radii of voids are derived. The sectional normalized area of the Poisson Voronoi tessellation is modelled by the Kiang function and by the exponential function. Two new survival functions with equivalent sectional radius are therefore derived; they represent an alternative to the survival function of voids between galaxies as given by the self-similar distribution. The spatial appearance of slices of the 2dF Galaxy Redshift Survey is simulated.