The X-ray luminosity function of very rich clusters and the luminosity-richness relation

For a sample of galactic clusters that includes richness class three, four, and five clusters, the significance of the luminosity-richness relation is estimated using nonparametric methods which are valid for any luminosity function. The Kolmogorov-Smirnov test is used to determine the significance at which the X-ray luminosities of clusters in one richness class are statistically equal to those in another. The a priori expectation that the high richness clusters are more luminous on average than lower richness objects is confirmed, but it is found that the luminosity function for clusters of richness class three or higher turns over for luminosities less than about 3 x 10 to the 44th ergs/s, while that for lower richness classes extends to at least an order of magnitude lower luminosity.