Basic properties of galaxy clustering in the light of recent results from the Sloan Digital Sky Survey

¹ Laboratoire de Physique Nucléaire et des Hautes Énergies, Université de Paris VI, 4 place Jussieu, Tour 33, Rez de Chaussée, 75252 Paris Cedex 05, France
² “Enrico Fermi Center”, via Panisperna 89 A, Compendio del Viminale, 00184 Rome, Italy
³ “Istituto dei Sistemi Complessi” CNR, via dei Taurini 19, 00185 Rome, Italy
⁴ Statistical Mechanics and Complexity Center – Istituto Nazionale Fisica della Materia, Unità di Roma 1, and Dipartimento di Fisica, Università di Roma “La Sapienza”, P.le A. Moro 2, 00185 Rome, Italy

Received: 20 June 2005
Accepted: 18 July 2005

Abstract

We discuss some of the basic implications of recent results on galaxy correlations published by the SDSS collaboration. In particular we focus on the evidence which has been recently presented for the scale and nature of the transition to homogeneity in the galaxy distribution, and results which describe the dependence of clustering on luminosity. The two questions are in fact strictly entangled, as the stability of the measure of the amplitude of the correlation function depends on the scale at which the mean density becomes well defined. We note that the recent results which indicate the convergence to well defined homogeneity in a volume equivalent to that of a sphere of radius 70 Mpc/h, place in doubt previous detections of “luminosity bias” from measures of the amplitude of the correlation function. We emphasize that the way to resolve these issues is to first use, in volume limited samples corresponding to different ranges of luminosity, the unnormalized two point statistics to establish the scale (and value) at which the mean density becomes well defined. We note also that the recent SDSS results for these statistics are in good agreement with those obtained by us through analyses of many previous samples, confirming in particular that the galaxy distribution is well described by a fractal dimension up to a scale of at least 20 Mpc/h. We discuss critically the agreement of this new data with current theoretical models.