X-RAY LUMINOSITY FUNCTIONS OF CLUSTERS OF GALAXIES

We show that clusters of galaxies must have a considerable intrinsic spread in their X-ray luminosities at given mass if they are formed bottom-up by direct gravitational instability. The distribution of luminosities at given mass take on the general form of a flat power law with a sharp upper cutoff, consistent with the recently obtained luminosity functions for Abell clusters of given richness classes. The quantitative features depend on the specific hierarchial cosmogony, with models including mass accretion after first collapse providing the best agreement. The same clustering mechanism, after integrating over mass, yields a steep overall luminosity function consistent with existing measurements.