X-ray emission from a complete sample of Abell clusters of galaxies.

The ROSAT All-Sky Survey (RASS) is used to investigate the X- ray properties of a complete sample of Abell clusters with measured redshifts and accurate positions. The sample comprises the 145 clusters within a 561 square degree region at high galactic latitude. The mean redshift is 0.17. This sample is especially well suited to be studied within the RASS since the mean exposure time is higher than average and the mean galactic column density is very low. These together produce a flux limit of about 4.2 x 10^-13^ erg cm^-2^ s^-1^ in the 0.5 to 2.5 keV energy band. Sixty-six (46%) individual clusters are detected at a significance level higher than 99.7% of which 7 could be chance coincidences of background or foreground sources. At redshifts greater than 0.3 six clusters out of seven (86%) are detected at the same significance level. The detected objects show a clear X-ray luminosity - galaxy count relation with a dispersion consistent with other external estimates of the error in the counts. By analyzing the excess of positive fluctuations of the X-ray flux at the cluster positions, compared with the fluctuations of randomly drawn background fields, it is possible to extend these results below the nominal flux limit. We find 80% of richness R >= 0 and 86% of R >= 1 clusters are X-ray emitters with fluxes above 1 x 10^13^ erg cm^-2^ s^-1^. Nearly 90% of the clusters meeting the requirements to be in Abell's statistical sample emit above the same level. We therefore conclude that almost all Abell clusters are real clusters and the Abell catalogue is not strongly contaminated by projection effects. We use the Kaplan-Meier product limit estimator to calculate the cumulative X-ray luminosity function. We show that the shape of the luminosity functions are similar for different richness classes, but the characteristic luminosities of richness 2 clusters are about twice those of richness 1 clusters which are in turn about twice those of richness 0 clusters. This result is another manifestation of the luminosity - richness relation for Abell clusters.