Redshift Dependence of the CMB Temperature from S-Z Measurements

We have determined the CMB temperature, $T(z)$, at redshifts in the range 0.023-0.546, from multi-frequency measurements of the S-Z effect towards 13 clusters. We extract the parameter $\alpha$ in the redshift scaling $T(z)=T_{0}(1+z)^{1-\alpha}$, which contrasts the prediction of the standard model ($\alpha=0$) with that in non-adiabatic evolution conjectured in some alternative cosmological models. The statistical analysis is based on two main approaches: using ratios of the S-Z intensity change, $\Delta I$, thus taking advantage of the weak dependence of the ratios on IC gas properties, and using directly the $\Delta I$ measurements. In the former method dependence on the Thomson optical depth and gas temperature is only second order in these quantities. In the second method we marginalize over these quantities which appear to first order in the intensity change. The marginalization itself is done in two ways - by direct integrations, and by a Monte Carlo Markov Chain approach. Employing these different methods we obtain two sets of results that are consistent with $\alpha=0$, in agreement with the prediction of the standard model.