Mismatch between X-Ray and Emission-weighted Temperatures in Galaxy Clusters: Cosmological Implications

The thermal properties of hydrodynamical simulations of galaxy clusters areusually compared to observations by relying on the emission-weightedtemperature T_ew, instead of on the spectroscopic X-ray temperature T_spec,which is obtained by actual observational data. In a recent paper Mazzotta etal. show that, if the cluster is thermally complex, T_ew fails at reproducingT_spec, and propose a new formula, the spectroscopic-like temperature, T_sl,which approximates T_spec better than a few per cent. By analyzing a set ofhydrodynamical simulations of galaxy clusters, we find that T_sl is lower thanT_ew by 20-30 per cent. As a consequence, the normalization of the M-T_slrelation from the simulations is larger than the observed one by about 50 percent. If masses in simulated clusters are estimated by following the sameassumptions of hydrostatic equilibrium and \beta--model gas density profile, asoften done for observed clusters, then the M-T relation decreases by about 40per cent, and significantly reduces its scatter. Based on this result, weconclude that using the observed M-T relation to infer the amplitude of thepower spectrum from the X-ray temperature function could bias low \sigma_8 by10-20 per cent. This may alleviate the tension between the value of \sigma_8inferred from the cluster number density and those from cosmic microwavebackground and large scale structure