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 thermal and kinetic Sunyaev-Zel'dovich (S-Z) effects on arcminute angular scales at millimeter wavelengths. Measurements of the amplitude of the thermal S-Z effect (Comptonization) can be combined with measurements of the X-ray brightness of the cluster to yield values for the Hubble 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 component of the peculiar velocity of the cluster. The confusion limit to 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 rich cluster, gamma approximately 10(-4), the contribution of confusion to the uncertainty in an estimate of H-0 will be 2DELTAgamma/gamma approximately 2% and 12%, respectively. The confusion limit to measurement of the kinetic S-Z effect has a broad minimum near 100 GHz. The estimated 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 photons. The estimated confusion limits assume that there is no beam dilution, and that the reference beam is sufficiently far from the cluster that it contains negligible S-Z signal. They will be larger otherwise.