Mismatch between X-ray and emission-weighted temperatures in galaxy clusters: Cosmological implications

The thermal properties of hydrodynamical simulations of galaxy clusters are usually compared to observations by relying on the emission-weighted temperature T<SUB>ew</SUB> instead of on the spectroscopic X-ray temperature T<SUB>spec</SUB>, which is obtained by actual observational data. In a recent paper, Mazzotta et al. show that if the intracluster medium is thermally complex, T<SUB>ew</SUB> fails at reproducing T<SUB>spec</SUB>. They propose a new formula, the spectroscopic-like temperature, T<SUB>sl</SUB>, which approximates T<SUB>spec</SUB> better than a few percent. By analyzing a set of hydrodynamical simulations of galaxy clusters, we find that T<SUB>sl</SUB> is lower than T<SUB>ew</SUB> by 20%-30%. As a consequence, the normalization of the M-T<SUB>sl</SUB> relation from the simulations is larger than the observed one by about 50%. If masses in simulated clusters are estimated by following the same assumptions of hydrostatic equilibrium and β-model gas density profile, as is often done for observed clusters, then the M-T relation decreases by about 40% and significantly reduces its scatter. On the basis of this result, we conclude that using the observed M-T relation to infer the amplitude of the power spectrum from the X-ray temperature function could bias low σ<SUB>8</SUB> by 10%-20%. This may alleviate the tension between the value of σ<SUB>8</SUB> inferred from the cluster number density and those from the cosmic microwave background and large-scale structure.