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 \leq 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 } h ^ { -1 } M _ { \odot } , 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 + 0.09 \Omega _ { 0 } } for flat low–density models and \sigma _ { 8 } = ( 0.60 \pm 0.04 ) \Omega _ { 0 } ^ { -0.48 + 0.17 \Omega _ { 0 } } for open models ( at the 90 % c.l .
) .

Subject headings : galaxies : clusters : general - cosmology : observations - cosmology : theory - large scale structure of universe .