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 (dec > 0 deg), at high Galactic latitudes (|b| > 20 deg), with measured redshifts z < 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 k S^(-alpha) with alpha=1.31 (+0.06)(-0.03) (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.