Measuring cluster peculiar velocities and temperatures at centimeter and millimeter wavelengths

I present a detailed investigation of issues related to the measurement of peculiar velocities and temperatures using Sunyaev-Zel'dovich (SZ) effects and estimate the accuracy to which peculiar velocities and gas temperatures of distant galaxy clusters could be measured. With muK sensitivity on arcminute scales at,several frequencies it will be possible to measure peculiar velocities to an accuracy of similar to130 km s(-1) and gas temperatures to better than 1 keV. The limiting factor for the accuracy of v(pec) is the presence of bulk motions within the galaxy cluster, even for apparently relaxed clusters. The accuracy of the temperature is mainly limited by noise. These results are independent of redshift, provided the clusters of interest are distant (zgreater than or similar to0.15). Using only three frequencies, the optimal strategy is to place one observing frequency in the Rayleigh-Jeans region (nu<40 GHz), one near 150 GHz, and the third at 300 GHz or higher. Measurements at the null of the thermal SZ effect are of marginal utility, other than as a foreground/background monitor.