The Observational Mass Function of Nearby Galaxy Clusters

We present a new determination of the mass function of galaxy clusters, based on optical virial mass estimates for a large sample of 152 nearby (z < 0.15) Abell--ACO clusters, as provided by Girardi et al. (1998). This sample includes both data from the literature and the new ENACS data. The resulting mass function is reliably estimated for masses larger than M_lim \simeq 4 \times 10^{14} \msun, while it is affected by sample incompleteness at smaller masses. We find N(>M_lim)=(6.3\pm 1.2) 10^{-6} (h^{-1} Mpc)^{-3} for cluster masses estimated within a 1.5 h^{-1} Mpc 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 sigma_8=(0.60\pm 0.04) Omega_0^{-0.46+0.09Omega_0} for flat low--density models and \sigma_8=(0.60\pm 0.04) Omega_0^{-0.48+0.17Omega_0} for open models (at the 90% c.l.)