Non-isothermality on the Sunyaev-Zel'dovich effect

We have proposed a method to calculate the real effect of non-isothermality on the Sunyaev-Zel'dovich effect (SZE). The non-isothermal effect is conventionally approximated by an emission-weighted temperature with the isothermal assumption or only considered the influence of the non-isothermal Compton y-parameter. We have compared the real SZE with those estimated by these two approximative methods for non-isothermal clusters with and without cooling flows. Two temperature profiles, the hybrid model and polytropic model, are considered for the clusters without cooling flows. For investigating the effect of cooling flows on the SZE, the A1835 cluster is taken for example. Temperature profiles in galaxy clusters strongly affect the SZE and consequently the estimated values of the Hubble constant. Different profiles result in very different error ranges for estimating the Hubble constant, ∼-3% to +10% for the hybrid model and ∼-10% to +40% for the polytropic model. Specially, the effect of cooling flows on determining the value of the Hubble constant is dramatic, ∼ + 45% for A1835, when the isothermal emission-weighted temperature is adopted.