Void probability as a function of the void's shape and scale-invariant models

Open Access
Publisher Website
Google Scholar
Abstract
Counts in cells, the probabilities Pi to have i galaxies inside a randomly chosen cell of volume V, and in particular the void probability P0, are related to higher order correlation functions and have received increasing attention as a tool to study 3D redshift catalogues, and to compare them with simulations or theoretical predictions. The dependence of counts in cells on the shape of the cell is studied here. A very concrete prediction is made concerning the void distribution for scale-invariant models, namely that the shape dependence can be obtained from the volume dependence by an appropriate scaling. This prediction is tested on a sample of the CfA catalogue, and good agreement is found. It is observed that the probability of voids is bigger for spherical cells than for elongated ones, whereas the probability of a cell to be occupied has a maximum for some elongated cells. A phenomenological scale-invariant model for the observed distribution of the counts in cells – an extension of the negative binomial distribution – is exhibited in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of the model is presented.

This publication has 0 references indexed in Scilit: