CONFUSION LIMITS TO THE MEASUREMENT OF THE SUNYAEV-ZELDOVICH EFFECTS IN CLUSTERS OF GALAXIES AT MILLIMETER WAVELENGTHS

We present estimates of the confusion limits to measurements of the th ermal and kinetic Sunyaev-Zel'dovich (S-Z) effects on arcminute angula r scales at millimeter wavelengths. Measurements of the amplitude of t he thermal S-Z effect (Comptonization) can be combined with measuremen ts of the X-ray brightness of the cluster to yield values for the Hubb le constant, H-0. The ratio of the kinetic and the thermal S-Z effects can be combined with the X-ray gas temperature to yield the radial co mponent of the peculiar velocity of the cluster. The confusion limit t o measurement of the thermal S-Z effect has minima at frequencies near 100 and 300 GHz. The estimated 1 sigma confusion limit to measurement of the Compton gamma parameter are DELTAgamma almost-equal-to 10(-6) and 6 x 10(-6), respectively. For a Compton parameter typical of a ric h cluster, gamma approximately 10(-4), the contribution of confusion t o the uncertainty in an estimate of H-0 will be 2DELTAgamma/gamma appr oximately 2% and 12%, respectively. The confusion limit to measurement of the kinetic S-Z effect has a broad minimum near 100 GHz. The estim ated 1 sigma confusion limit to measurement of the radial component of the peculiar velocity is DELTAupsilon(r) almost-equal-to 50 (tau/0.01 )-1 km s-1, where tau is the optical depth for scattering of the CMB p hotons. The estimated confusion limits assume that there is no beam di lution, and that the reference beam is sufficiently far from the clust er that it contains negligible S-Z signal. They will be larger otherwi se.