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

We present a new method aiming to simplify 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 modeling. We illustrate the methodology for the case of a 100 deg2 XMM survey having a sensitivity of ~10^{-14} ergs/s/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 care to the realistic modeling 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 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 similarly as the traditional mass function (dn/dM/dz) for the purely cosmological parameters, but better constrains 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.