The Local Cluster Mass Function from Optical Virial Analysis

We analyze in an homogeneous way a sample of 170 nearby galaxy clusters (z < 0.15) which includes both data from the literature and recent data from the ENACS survey. Under the assumption that mass follows galaxy distribution, we compute cluster masses by applying the virial theorem to member galaxies. The above assumption is supported, a posteriori, by the good agreement between our optical mass estimates and those derived from X-ray analyses, which are free from any a priori assumption about the mass distribution. By resampling our 152 Abell-ACO clusters according to the richness class frequencies of EDCC catalog, we obtain a cluster sample representative of the Universe. The resulting mass function is reliably estimated for masses larger than Mlim ≍ 4 × 1014 msun, while it is affected by sample incompleteness at smaller masses. We find N(> Mlim) = (6.3 +/- 1.2) 10^{-6} (h^{-1} Mpc)^{-3} for cluster masses estimated within a 1.5 h radius. Our mass function is intermediate between the two previous estimates by Bahcall & Cen (1993) and by Biviano et al. (1993). Based on the Press-Schechter approach, we use this mass function to constrain the amplitude of the fluctuation power spectrum at the cluster scale. After suitably convolving the PS predictions with observational errors on cluster masses and COBE-normalizing the fluctuation power spectrum, we find σ_8 = (0.60 +/- 0.04) Ω_0^{-0.46 + 0.09ω_0} for flat low-density models and σ_8 = (0.60 +/- 0.04) Ω_0^{-0.48 + 0.17Ω_0} for open models (at the 90% c.l.).