Galaxy distribution and extreme-value statistics

¹  Program for Evolutionary Dynamics, Harvard University - Cambridge, MA 02138, USA
²  Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi - Piazzale del Viminale 1, 00184 Rome, Italy, EU
³  Istituto dei Sistemi Complessi CNR - Via dei Taurini 19, 00185 Rome, Italy, EU
⁴  Institute of Astronomy, St. Petersburg State University - Staryj Peterhoff, 198504, St. Petersburg, Russia

Received: 23 August 2009
Accepted: 12 November 2009

Abstract

We consider the conditional galaxy density around each galaxy, and study its fluctuations in the newest samples of the Sloan Digital Sky Survey Data Release 7. Over a large range of scales, both the average conditional density and its variance show a non-trivial scaling behavior, which resembles criticality. The density depends, for 10 ≤ r ≤ 80 Mpc/h, only weakly (logarithmically) on the system size. Correspondingly, we find that the density fluctuations follow the Gumbel distribution of extreme-value statistics. This distribution is clearly distinguishable from a Gaussian distribution, which would arise for a homogeneous spatial galaxy configuration. We also point out similarities between the galaxy distribution and critical systems of statistical physics.