The cosmological analysis of X-ray cluster surveys – I. A new method for interpreting number counts




We present a new method aimed at simplifying the cosmological analysis of X-ray cluster surveys. It is based on purely instrumental observable quantities considered in a two-dimensional X-ray colour–magnitude diagram (hardness ratio versus count rate). The basic principle is that even in rather shallow surveys, substantial information on cluster redshift and temperature is present in the raw X-ray data and can be statistically extracted; in parallel, such diagrams can be readily predicted from an ab initio cosmological modelling. We illustrate the methodology for the case of a 100-deg2XMM survey having a sensitivity of ∼10−14 erg s−1 cm−2 and fit at the same time, the survey selection function, the cluster evolutionary scaling relations and the cosmology; our sole assumption – driven by the limited size of the sample considered in the case study – is that the local cluster scaling relations are known. We devote special attention to the realistic modelling of the count-rate measurement uncertainties and evaluate the potential of the method via a Fisher analysis. In the absence of individual cluster redshifts, the count rate and hardness ratio (CR–HR) method appears to be much more efficient than the traditional approach based on cluster counts (i.e. dn/dz, requiring redshifts). In the case where redshifts are available, our method performs similar to the traditional mass function (dn/dM/dz) for the purely cosmological parameters, but constrains better parameters defining the cluster scaling relations and their evolution. A further practical advantage of the CR–HR method is its simplicity: this fully top-down approach totally bypasses the tedious steps consisting in deriving cluster masses from X-ray temperature measurements.