Systematic Bias in an Estimate of the Cluster Mass and the Fluctuation Amplitude from Cluster Abundance Statistics

Abstract

Abstract We revisit an 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, $M_\mathrm{vir}$. Mazzotta et al. (2004, MNRAS, 354, 10) recently pointed out the possibility that $\alpha_{M} = M_\mathrm{vir,\, spec} / M_\mathrm{vir}$ is systematically lower than unity. We performed a statistical analysis by combining the latest X-ray cluster sample and the improved theoretical models, and found that $\sigma_8 \sim 0.76 \pm 0.01 + 0.50 \, (1-\alpha_{M})$ for $0.5 \le \alpha_{M} \le 1$, where the quoted errors are only statistical. 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.