ROSAT observations of distant, optically selected galaxy clusters.

Evolution of the X-ray cluster luminosity function is investigated through X-ray observations of the Couch et al. catalogue of distant, optically selected galaxy clusters. A subset of 14 clusters provides a statistically complete sample, with mean redshift z^bar^ = 0.42, and a typical Abell richness of class 1-2. Observations of 12 of these clusters were secured using the ROSAT satellite in pointed mode; the remaining two clusters are analysed using data from the All Sky Survey. The X-ray emission from these clusters is surprisingly weak. The cluster luminosities are less than 5 X 10^43^ erg s^-1^ in all but two cases. We use a maximum-likelihood method to perform a quantitative comparison between our distant cluster luminosities and the present-day X-ray luminosity function derived by Henry et al. from the Einstein Extended Medium Sensitivity Survey. In the simplest case, where there is a direct relationship between optical richness and X-ray luminosity, our results imply a rise in the amplitude of the luminosity function by almost an order of magnitude since z~0.4. Even allowing for a significant scatter in the richness-L_x_ correlation, as observed locally, the distant data are inconsistent with the present-day luminosity function at the 3σ level. Our ROSAT data thus confirm the negative evolution of the luminosity function seen in the Einstein EMSS survey, and suggest that the steep slope in the high-redshift function may flatten off at luminosities below 10^44^ erg s^-1^.