The mass function of clusters of galaxies

The mass function of clusters of galaxies is derived separately from optical and X-ray observations of their respective properties. The mass function was extended to the faint end, to lower masses than the rich clusters, using small groups of galaxies. The derived mass function is within the mass range from approximately 10 exp 12 to not less than 10 exp 15/h solar masses. The deduced density range n is approximately 10 exp -2 to 10 exp -8 cubic h/cubic Mpc. The observed shape of the mass function exhibits a shallow power-law decrease with mass at the faint end, and a steep exponential decrease with mass at the massive end. A summary of some constraints placed by the observed mass function on current cosmological models is presented.