[Paper Review] Breaking of self-averaging properties and selection effects in the Luminous Red Galaxies sample

Francesco Sylos Labini|arXiv (Cornell University)|Nov 22, 2010

Scientific Research and Discoveries4 references4 citations

TL;DR

This study investigates statistical self-averaging breakdown in the Sloan Digital Sky Survey's Luminous Red Galaxy (LRG) sample by analyzing the probability density function (PDF) of galaxy counts in spheres. It finds systematic deviations in PDF shape and peak location across regions, indicating major selection effects or intrinsic inhomogeneities—implying that volume-averaged quantities like correlation functions are unreliable, with over 20% of galaxies potentially unobserved due to non-smooth redshift-dependent selection.

ABSTRACT

We study the statistical properties of the Luminous Red Galaxies sample from the Sloan Digital Sky Survey. In particular we test, by determining the probability density function (PDF) of galaxy (conditional) counts in spheres, whether statistical properties are self-averaging within the sample. We find that there are systematic differences in the shape of the PDF and in the location of its peak, signaling that there are major systematic effects in the data which make the estimation of volume average quantities unreliable within this sample. We discuss that these systematic effects are related to the fluctuating behavior of the redshift counts which can be originated by intrinsic fluctuations in the galaxy density field or by observational selection effects. The latter possibility implies that more than 20 % of the galaxies have not been observed and that such a selection should not be a smooth function of redshift.

Motivation & Objective

• To test whether statistical properties in the LRG sample are self-averaging, a fundamental requirement for reliable volume averaging.
• To determine whether the irregular redshift-dependent number density n(z) arises from intrinsic fluctuations or observational selection effects.
• To assess the reliability of two-point correlation functions and average conditional densities derived from the LRG sample.
• To evaluate whether the observed n(z) behavior invalidates standard assumptions of volume-limited sampling in cosmological clustering studies.
• To challenge the assumption that the LRG sample is a representative, volume-limited tracer of large-scale structure.

Proposed method

• Computed the probability density function (PDF) of conditional galaxy counts in spheres of radius r centered on each LRG to assess local statistical fluctuations.
• Compared PDFs across different regions of the LRG sample to test for spatial invariance and self-averaging.
• Used conditional counts N_i(r) as a local, geometry-independent measure of clustering, avoiding biases from global sample boundaries.
• Analyzed the behavior of the PDF peak and shape across redshift shells to detect systematic deviations from expected statistical homogeneity.
• Contrasted results with mock catalogs from LCDM simulations to test whether observed n(z) behavior could be due to random sampling effects.
• Evaluated the impact of redshift-dependent selection on correlation function estimation using data-random pair-counting methods with non-Poissonian random samples.

Experimental results

Research questions

• RQ1 Is the LRG sample self-averaging, such that local statistical properties reliably represent global averages?
• RQ2 Do the observed irregularities in the redshift number density n(z) stem from intrinsic large-scale fluctuations or from observational selection effects?
• RQ3 To what extent do non-smooth, redshift-dependent selection effects invalidate the use of volume-averaged statistics in the LRG sample?
• RQ4 Can the observed n(z) behavior be explained by random sampling effects, or does it indicate systematic deviations from statistical homogeneity?
• RQ5 How robust are two-point correlation functions and average conditional densities when self-averaging is broken?

Key findings

• The PDF of galaxy counts in spheres shows systematic differences in shape and peak location across different regions of the LRG sample, indicating a breakdown of self-averaging.
• The observed irregular and decaying n(z) behavior cannot be explained by a smooth redshift-dependent selection function, suggesting either major observational selection effects or intrinsic inhomogeneities.
• More than 20% of galaxies may be unobserved due to non-smooth, redshift-dependent selection effects, which are not accounted for in standard statistical treatments.
• The average conditional density cannot be reliably determined at scales of ~100 Mpc/h due to the breakdown of self-averaging, contradicting claims of uniformity at those scales.
• The observed behavior is incompatible with a transition to uniformity at ~100 Mpc/h, challenging previous interpretations of large-scale structure in the LRG sample.
• The results imply that current LRG-based measurements of correlation functions and large-scale clustering may be systematically biased due to unaccounted selection effects or non-stationary fluctuations.