Temperature Bias in Measurements of The Hubble Constant Using The Sunyaev-Zeldovich Effect

Measurements of the Hubble constant to distant galaxy clusters using the Sunyaev-Zeldovich effect are systematically low in comparison to values obtained by other means. These measurements usually assume a spherical isothermal β model for the intracluster medium (ICM). Formation processes and recent mergers guarantee that real clusters are neither spherical nor isothermal. We present the results of a statistical analysis of temperature bias in H0 determinations in a sample of 27 numerically simulated X-ray clusters drawn from a ΛCDM model at z=0.5 (the sample is online at http://sca.ncsa.uiuc.edu). We employ adaptive mesh refinement to provide high resolution (15.6 hkpc) in cluster cores which dominate the X-ray and radio signals (sample images on line at http://cosmos.ucsd.edu/∼wenlin/SZ/sz cluster.html). The clusters possess a variety of shapes and merger states which are computed self-consistently in a cosmological framework assuming adiabatic gas dynamics. We derive the value of H0 by computing the angular diameter distance to each cluster along three orthogonal lines of sight. Fitting synthetic X-ray and y-parameter maps to the standard isothermal beta model, we find a broad, skewed distribution in f ≡ H0(SZ)/H0(actual) with a mean, median, and standard deviation of 0.89, 0.83 and 0.32 respectively, where H0(SZ) is the value of H0 derived by using Sunyaev-Zeldovich effect method and H0(actual) is the value used in the cosmological simulation. We find that the clusters’ declining temperature profiles systematically lower estimates of H0 by 10% to 20%. The declining temperature profile of our adiabatic system is consistent with the result including radiative cooling and supernovae feedback (Loken et al. 2002). We thereby introduce a non-isothermal β model as an improvement. Applying the non-isothermal β model to the refined sample with well-fitted temperature profile, the value of f improves 9% relative to the actual value. The study of the morphology and the Department of Astronomy, University of Illinois at Champaign Urbana, Urbana, IL 61801, U.S.A. CASS, University of California at San Diego, La Jolla, CA 92093, U.S.A. The Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, UK