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 greater than or equal to 0 degrees), at high Galactic latitudes (\b\ greater than or equal to 20 degrees), with measured redshifts z less than or equal to 0.3 and fluxes higher than 4.4 x 10-(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 1 sigma error). We find the cumulative log N-log S distribution of clusters to follow a power law kappa S-alpha with alpha = 1.31(-0.03)(+0.06) (errors are the 10th and 90th percentiles) down to fluxes of 2 x 10(-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 log N-log S 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.