The ROSAT Brightest Cluster Sample - I. The compilation of the sample and the cluster log N-log S distribution

We present a 90 per cent flux-complete sample of the 201 X-ray-brightest clusters of galaxies in the northern hemisphere (delta>=0 deg), at high Galactic latitudes (|b|>=20 deg), with measured redshifts z<=0.3 and fluxes higher than 4.4x10^-12 erg cm^-2 s^-1 in the 0.1-2.4 keV band. The sample, called the ROSAT Brightest Cluster Sample (BCS), is selected from ROSAT All-Sky Survey data and is the largest X-ray-selected cluster sample compiled to date. In addition to Abell clusters, which form the bulk of the sample, the BCS also contains the X-ray-brightest Zwicky clusters and other clusters selected from their X-ray properties alone. Effort has been made to ensure the highest possible completeness of the sample and the smallest possible contamination by non-cluster X-ray sources. X-ray fluxes are computed using an algorithm tailored for the detection and characterization of X-ray emission from galaxy clusters. These fluxes are accurate to better than 15 per cent (mean 1sigma error). We find the cumulative logN-logS distribution of clusters to follow a power law kappa S^alpha with alpha=1.31^+0.06_-0.03 (errors are the 10th and 90th percentiles) down to fluxes of 2x10^-12 erg cm^-2 s^-1, i.e. considerably below the BCS flux limit. Although our best-fitting slope disagrees formally with the canonical value of -1.5 for a Euclidean distribution, the BCS logN-logS distribution is consistent with a non-evolving cluster population if cosmological effects are taken into account. Our sample will allow us to examine large-scale structure in the northern hemisphere, determine the spatial cluster-cluster correlation function, investigate correlations between the X-ray and optical properties of the clusters, establish the X-ray luminosity function for galaxy clusters, and discuss the implications of the results for cluster evolution.