Point field models for the galaxy point pattern

Modelling the singularity of the two-point correlation function

¹ Mathematical Department, Silesian University at Opava, Bezručovo nám. 13, 74601 Opava 1, Czech Republik e-mail: Martin.Snethlage@math.slu.cz
² Observatori Astrònomic, Universitat de València, 46100 Burjassot, Spain
³ Institut für Stochastik, TU Bergakademie Freiberg, Bernhard-von-Cotta-Str. 2, 09596 Freiberg, Germany e-mail: stoyan@orion.hrz.tu-freiberg.de
⁴ Tartu Observatory, Tõravere, 61602, Estonia e-mail: saar@aai.ee

Corresponding author: V. J. Martínez, Vicent.Martinez@uv.es

Received: 7 December 2001
Accepted: 8 April 2002

Abstract

There is empirical evidence that the two-point correlation function of the galaxy distribution follows, for small scales, reasonably well a power-law expression with γ between 1.5 and 1.9. Nevertheless, most of the point field models suggested in the literature do not have this property. This paper presents a new class of models, which is produced by modifying point fields commonly used in cosmology to mimic the galaxy distribution, but where is too large. The points are independently and randomly shifted, leading to the desired reduction of the value of γ.