What can the spatial distribution of galaxy clusters tell about their scaling relations?. (arXiv:1306.1399v1 [astro-ph.CO])

What can the spatial distribution of galaxy clusters tell about their scaling relations?. (arXiv:1306.1399v1 [astro-ph.CO]):
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. As an example, we use the
mass-X ray luminosity of galaxy clusters. We define the luminosity-weighted
power spectrum and introduce the luminosity power spectrum as a direct
assessment of the clustering of 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 measure the luminosity-weighted and the
luminosity power spectrum of galaxy clusters. By means of a Fisher matrix
analysis, we quantify the content of information (by means of a Figure-of
Merit) encoded in the amplitude, shape and full-shape of these probes. 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 only one order of magnitude below the
value encoded in X-ray luminosity function estimated from the same sample. This
is a significant improvement with respect to the FoM obtained from the
estimates of the unweighted power spectrum. We therefore suggest future
clustering analysis of galaxy clusters to take advantage of the luminosity
power spectrum when aiming at simultaneously constraining cosmological and
astrophysical parameters (Abridged)