Systematic Errors in the Determination of Hubble Constant due to the Asphericity and Nonisothermality of Clusters of Galaxies

Abstract

We present statistical studies on the systematic errors in the determination of the Hubble constant H0 from joint analyses of X-ray and the Sunyaev-Zel'dovich (SZ) effect of clusters of galaxies. We focus on the effects of their triaxiality and nonisothermality. From the triaxial model of dark matter halos obtained from numerical simulations, we derive the distribution of the intracluster gas under the assumption of the hydrodynamic equilibrium. Both the isothermal and the polytropic gases are investigated. We run Monte Carlo simulations to generate samples of clusters according to the distributions of their masses, axial ratios, concentration parameters, and line-of-sight directions. The estimation of H0 is done by fitting X-ray and SZ profiles of a triaxial cluster with the isothermal and spherical β model. We find that for a sample of clusters with M = 1014 h-1 M☉ and z = 0.1, the estimated H0 is positively biased with H(estimated) ≈ 1.05H0(true) and H(estimated) ≈ 1.05H0(true) for the isothermal case. For the polytropic case with γ = 1.15, the bias is large with H(estimated) ≈ 1.35H0(true) and H(estimated) ≈ 3H0(true). For a mass-limited sample of clusters with Mlim = 1013 h-1 M☉, the results are similar. On the other hand, such a large overestimation has not been seen in real observations. It is noticed that the β-value for observed clusters is within the range of 0.5-0.8. Considering only the subsample in Monte Carlo simulations with β in the range of 0.5-0.8, we have H(estimated) = 1.002H0(true) and H(estimated) = 0.994H0(true) for the isothermal and polytropic cases, respectively. We further find that the value of β is more sensitive to the intrinsic asphericity of clusters than the axial ratio of two-dimensional X-ray images η is. Limiting to clusters with β ≥ 0.5 essentially excludes highly aspherical clusters from the sample. From this subsample of clusters, we can get a fair estimate on H0.