What can the spatial distribution of galaxy clusters tell about their scaling relations?^⋆

Argelander Institute für Astronomie, Universität Bonn, auf dem Hügel 71, 53121 Bonn, Germany INAF Osservatorio Astronomico di Roma, via di Frascati 33 00040 Monte Porzio Catone Italy
e-mail: abalan@astro.uni-bonn.de

Received: 6 June 2013
Accepted: 20 January 2014

Abstract

Context. The clustering of galaxy clusters is sensitive not only to the parameters characterizing a given cosmological model, but also to the links between cluster intrinsic properties (e.g., the X-ray luminosity, X-ray temperature) and the total cluster mass. These links, referred to as the cluster scaling relations, represent the tip of the iceberg of the so-called cross-roads between cosmology and astrophysics on the cluster scale.

Aims. In this paper we aim to quantify the capability of the inhomogeneous distribution of galaxy clusters, represented by the two-point statistics in Fourier space, to retrieve information on the underlying scaling relations. To that end, we make a case study using the mass–X-ray luminosity scaling relation for galaxy clusters and study its impact on the clustering pattern of these objects.

Methods. To characterize the clustering of galaxy clusters, we define the luminosity-weighted power spectrum and introduce the luminosity power spectrum as direct assessment of the clustering of the property of interest, in our case, the cluster X-ray luminosity. Using a suite of halo catalogs extracted from N-body simulations and realistic estimates of the mass–X-ray luminosity relation, we measured these statistics with their corresponding covariance matrices. By carrying out a Fisher matrix analysis, we quantified the content of information (by means of a figure of merit) encoded in the amplitude, shape, and full shape of our probes for two-point statistics.

Results. The full shape of the luminosity power spectrum, when analyzed up to scales of k ~ 0.2 h Mpc^-1, yields a figure of merit that is two orders of magnitude above the figure obtained from the unweighted power spectrum, and only one order of magnitude below the value encoded in X-ray luminosity function estimated from the same sample. This is a significant improvement over the analysis developed with the standard (i.e., unweighted) clustering probes.

Conclusions. The measurements of the clustering of galaxy clusters and its explicit dependence on the cluster intrinsic properties can contribute to improving the degree of knowledge regarding the underlying links between cluster observables and cluster masses. We therefore suggest future clustering analysis of galaxy clusters to implement the weighted statistics and especially the luminosity (or any other property of interest) power spectrum when aiming at simultaneously constraining cosmological and astrophysical parameters.