4.3. Mass function of clusters of galaxies

Masses of clusters of galaxies can be determined from the velocity dispersion of its member galaxies, or on the basis of their X-ray emission (using the hot gas as an indicator of the velocity dispersion in clusters), or else from the gravitational lens effect. Using masses of clusters and their abundance it is possible to calculate the number of clusters of different mass, N( > M). This mass function is usually expressed in units of h^-1M₀ in a sphere of radius 1.5 h^-1 Mpc. The cluster mass function was derived by Bahcall & Cen [3], and also by Girardi [27]. The function characterizes the distribution of systems of galaxies at the present epoch. There exist estimates of the abundance of clusters at high redshifts, but they are still very uncertain. The function N( > M), and its specific value, N( > 10¹⁴M₀), can be used to constrain cosmological parameters. We shall use this constraint in the next Section.