The X-ray luminosity function of Abell clusters

X-ray sources identified with Abell clusters of galaxies in distance classes less than or equal to 3 give a quantitative estimate of the volume luminosity function for those clusters emitting between 10 to the 44th and 10 to the 45th power ergs/s in X-rays. At higher luminosities, tentative identifications with more distant clusters can be interpreted at least as an upper limit. This limit allows a smooth extension of the luminosity function, but with a fairly steep decrease in the range from 10 to the 45th to 10 to the 46th power ergs/s. No direct information is available for luminosities less than 10 to the 44th power ergs/s because current X-ray surveys are limited to nearby distances with very few Abell clusters; however, constraints at the low-luminosity end can be set by considering the total volume density of Abell clusters and the upper limit to the numbers of unidentified X-ray sources. The luminosity function must flatten or turn over below 10 to the 44th power ergs/s; therefore, counts of distant X-ray clusters to such a faint intrinsic luminosity can yield cosmological information.