We revisit the estimate of the mass fluctuation amplitude , \sigma _ { 8 } , from the observational X-ray cluster abundance .
In particular , we examine the effect of the systematic difference between the cluster virial mass estimated from the X-ray spectroscopy , M _ { \mathrm { vir, spec } } , and the true virial mass of the corresponding halo , M _ { \mathrm { vir } } . \citet mazzotta04 recently pointed out the possibility that \alpha _ { \mathrm { M } } = M _ { \mathrm { vir, spec } } / M _ { \mathrm { vir } } is systematically lower than unity .
We perform the statistical analysis combining the latest X-ray cluster sample and the improved theoretical models and find that \sigma _ { 8 } \sim 0.76 \pm 0.01 + 0.50 ( 1 - \alpha _ { \mathrm { M } } ) for 0.5 \leq \alpha _ { \mathrm { M } } \leq 1 , where the quoted errors are statistical only .
Thus if \alpha _ { \mathrm { M } } \sim 0.7 , the value of \sigma _ { 8 } from cluster abundance alone is now in better agreement with other cosmological data including the cosmic microwave background , the galaxy power spectrum and the weak lensing data .
The current study also illustrates the importance of possible systematic effects in mapping real clusters to underlying dark halos which changes the interpretation of cluster abundance statistics .