Abstract
The angular-diameter distance DA of a galaxy cluster can be measured by combining its X-ray emission with the cosmic microwave background fluctuation due to the Sunyaev–Zeldovich (SZ) effect. The application of this distance indicator usually assumes that the cluster is spherically symmetric, the gas is distributed according to the isothermal β-model, and the X-ray temperature is an unbiased measure of the electron temperature. We test these assumptions with galaxy clusters extracted from an extended set of cosmological N-body/hydrodynamical simulations of a Λ cold dark matter concordance cosmology, which include the effect of radiative cooling, star formation and energy feedback from supernovae. We find that, due to the temperature gradients which are present in the central regions of simulated clusters, the assumption of isothermal gas leads to a significant underestimate of DA. This bias is efficiently corrected by using the polytropic version of the β-model to account for the presence of temperature gradients. In this case, once irregular clusters are removed, the correct value of DA is recovered with a ∼5 per cent accuracy on average, with a ∼20 per cent intrinsic scatter due to cluster asphericity. This result is valid when using either the electron temperature or a spectroscopic-like temperature. Instead When using the emission-weighted definition for the temperature of the simulated clusters, DA is biased low by ∼20 per cent. We discuss the implications of our results for an accurate determination of the Hubble constant H0 and of the density parameter Ωm. We find that, at least in the case of ideal (i.e. noiseless) X-ray and SZ observations extended out to r500, H0 can be potentially recovered with exquisite precision, while the resulting estimate of Ωm, which is unbiased, has typical errors ΔΩm≃ 0.05.
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