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

Abstract

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. 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. 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. The full shape of the luminosity power spectrum, when analyzed up to scales of k~0.2 h/Mpc, yields a figure of merit which 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. 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 the cluster masses (Abridged).

12 pages, 9 figures. Accepted for publication in Astronomy and Astrophysics

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