| © CAMBRIDGE UNIVERSITY PRESS 1999
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3.8. The X-Ray Luminosity Function of Clusters
The X-ray luminosity function of clusters (the number density of clusters with X-ray luminosity Lx to Lx + dLx) is approximately (Edge et al. 1990)
| (40) |
for h = 0.5, where Lx is the 2-10-keV X-ray luminosity in units of ergs-1 (for h = 0.5). The luminosity function can also be approximated as a power law (Edge et al. 1990)
| (41) |
The number of X-ray clusters with X-ray luminosity brighter than Lx is approximately
| (42) |
The observed evolution of the X-ray cluster luminosity function suggests
fewer high-luminosity clusters in the past
(z 
0.5)
(Edge et al. 1990,
Henry et al. 1992).
Additional data is required,
however, to confirm and better assess the cluster evolution.
3.9. Cooling Flows in Clusters
Cooling flows are common at the dense cores of rich clusters;
X-ray images and spectra of ~ 50% of clusters suggest that the gas
is cooling rapidly at their centers
(Sarazin 1986;
Fabian 1992).
Typical inferred cooling rates are ~ 100
/ yr. The gas cools
within r 
100h-1 kpc of the cluster center
(generally centered on the brightest galaxy).
The cooling flows often show evidence for optical line emission,
blue stars, and in some cases evidence for colder material in HI
or CO emission, or X-ray absorption.