Astronomy & Astrophysics

Free access article

Issue		A&A Volume 429, Number 1, January I 2005
Page(s)		65 - 74
Section		Cosmology (including clusters of galaxies)
DOI		10.1051/0004-6361:20041469

A&A 429, 65-74 (2005)
DOI: 10.1051/0004-6361:20041469

Cosmological distances and fractal statistics of galaxy distribution

M. B. Ribeiro

Physics Institute, University of Brazil-UFRJ, CxP 68532, CEP 21945-970, Rio de Janeiro, Brazil
e-mail: mbr@if.ufrj.br

(Received 15 June 2004 / Accepted 6 August 2004)

Abstract
This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various distance definitions are used to calculate the differential density $\gamma$ and the integral differential density $\gamma^\ast$ of the dust distribution in the Einstein-de Sitter cosmology. The main results are as follows: (1) the choice of distance plays a crucial role in determining the scale where relativistic corrections must be taken into account, as both $\gamma$ and $\gamma^\ast$ are strongly affected by such a choice; (2) inappropriate distance choices may lead to failure to find evidence of a galaxy fractal structure when one calculates those quantities, even if such a structure does occur in the galaxy distribution; (3) the comoving distance and the distance given by Mattig's formula are unsuitable to probe for a possible fractal pattern as they render $\gamma$ and $\gamma^\ast$ constant for all redshifts; (4) a possible galaxy fractal system at scales larger than 100 Mpc ( $z \approx 0.03$ ) may only be found if those statistics are calculated with the luminosity or redshift distances, as they are the ones where $\gamma$ and $\gamma^\ast$ decrease at higher redshifts; (5) Célérier & Thieberger's (2001) critique of Ribeiro's (1995) earlier study are rendered impaired as their objections were based on misconceptions regarding relativistic distance definitions.

Key words: cosmology: theory -- cosmology: large-scale structure of the Universe -- cosmology: observation -- galaxies: distances and redshifts -- galaxies: statistics

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