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 \beta 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 H _ { 0 } determinations in a sample of 27 numerically simulated X-ray clusters drawn from a \Lambda CDM 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 h ^ { -1 } kpc ) in cluster cores which dominate the X-ray and radio signals ( sample images on line at http : //cosmos.ucsd.edu/ \sim 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 H _ { 0 } 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 \equiv H _ { 0 } ( SZ ) / H _ { 0 } ( actual ) with a mean , median , and standard deviation of 0.89 , 0.83 and 0.32 respectively , where H _ { 0 } ( SZ ) is the value of H _ { 0 } derived by using Sunyaev-Zeldovich effect method and H _ { 0 } ( actual ) is the value used in the cosmological simulation .
We find that the clusters ’ declining temperature profiles systematically lower estimates of H _ { 0 } 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 \beta model as an improvement .
Applying the non-isothermal \beta 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 clumping effects conclude that these two factors combine to induce scatter in f of \pm 30 \% .