The mass function of clusters of galaxies

The mass function of clusters of galaxies is determined from recent optical and X-ray observations. The function is derived separately from optical and from X-ray data of the clusters. Both measures yield the same mass function within the expected uncertainties. The function is extended to the faint end using small groups of galaxies. The resulting mass function of groups and clusters of galaxies ranges from M ∼ 10¹² to ≥10¹⁵ h^-1 M⊙ and covers the density range n ∼ 10^-2 to 10^-8 h³ Mpc^-3. It can be represented analytically by n(>M) = 4 × 10^-5 (M/M*)^-1 exp (-M/M*) h³ Mpc^-3, with M* = (1.8 ± 0.3) × 10¹⁴ h^-1 M⊙; M is the mass within 1.5 h^-1 Mpc radius sphere around the cluster center. Some constraints placed by the observed mass function on current cosmological models are briefly summarized. The observed function appears to be inconsistent with standard (Ω = 1) CDM models (with any bias parameter), but is consistent with low-density (Ω ∼ 0.25) CDM models (with or without a cosmological constant) as well as with primeval baryonic isocurvature models with Ω ∼ 0.2.