Order statistics applied to the most massive and most distant galaxy clusters

TL;DR

This paper develops an analytic framework for using order statistics of galaxy clusters in mass and redshift to test cosmological models, providing new tools for survey analysis and consistency checks.

Contribution

It introduces the first analytic method for calculating joint distributions of galaxy cluster order statistics, enhancing cosmological constraints and survey assessments.

Findings

Order statistics steepen with increasing order, improving constraining power.

Mass order statistics are sensitive to matter density and fluctuation normalization.

Redshift order statistics are sensitive to the universe's geometric evolution.

Abstract

In this work we present for the first time an analytic framework for calculating the individual and joint distributions of the n-th most massive or n-th highest redshift galaxy cluster for a given survey characteristic allowing to formulate LCDM exclusion criteria. We show that the cumulative distribution functions steepen with increasing order, giving them a higher constraining power with respect to the extreme value statistics. Additionally, we find that the order statistics in mass (being dominated by clusters at lower redshifts) is sensitive to the matter density and the normalisation of the matter fluctuations, whereas the order statistics in redshift is particularly sensitive to the geometric evolution of the Universe. For a fixed cosmology, both order statistics are efficient probes of the functional shape of the mass function at the high mass end. To allow a quick assessment of both order statistics, we provide fits as a function of the survey area that allow percentile estimation with an accuracy better than two per cent. Furthermore, we discuss the joint distributions in the two-dimensional case for different combinations of order. Having introduced the theory, we apply the order statistical analysis to the SPT massive cluster sample and MCXC catalogue and find that the ten most massive clusters in the sample are consistent with LCDM and the Tinker mass function. In turn, by assuming the LCDM reference cosmology, order statistics can also be utilised for consistency checks of the completeness of the observed sample and of the modelling of the survey selection function. [abridged]