Robustness of the Sunyaev-Zel’dovich Effect as a Measure of the Hubble Constant

After inversing the x-ray surface brightness of the cooling flow cluster Abell 1689 through the isothermal β model, the isothermal double β model and the x-ray surface brightness distribution model derived from the universal dark matter density profile, we calculate the electron distribution and the Sunyaev-Zel'dovich (SZ) effect of the cluster. The resulting temperature decrements, which are inversely proportional to the square root of H₀, are very different for the three models, with uncertainty of 15%. Thus, the SZ/x-ray route can not be taken as a precise measurement of H₀ until further observations (e.g. from the satellite AXAF) constrain well the amount and distribution of cluster gas.