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Systematic bias in the estimate of cluster mass and the fluctuation amplitude from cluster abundance statistics

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_{vir, spec}, and the true virial mass of the corresponding halo, M_{vir}. Mazzotta et al. (2004) recently pointed out the possibility that alpha_M = M_{vir, spec}/M_{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 +/- 0.01 + 0.50 (1-alpha_M) for 0.5 \le alpha_M \le 1, where the quoted errors are statistical only. Thus if alpha_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.