Estimates of Confusion and Gravitational Lensing Limits in Sunyaev-Zel'dovich Increment Measurements

We present estimates of the confusion limit of measurements of the Sunyaev-Zel'dovich effect (SZ) increment near its peak intensity based on Monte Carlo simulations of sub-millimetre observations of galaxy clusters. Specifically, we evaluate the contribution of gravitational lensing of high redshift background sources by a target cluster to its inferred SZ signal. We find that the background confusion limit is 0.6 mJy per beam without any lensing. With gravitational lensing, the confusion limit increases to 0.9 mJy per beam. Removing bright sources in the gravitationally lensed fields decreases the confusion limit to 0.7 mJy per beam, essentially background levels. These limits are found by removing exceptionally poor fits to the expected SZ profile, which are due to the different structure of the SZ and lensing angular profiles. We conclude that experiments designed to measure the SZ increment must have high enough angular resolution to identify background point sources while surveying enough of the sky to determine the SZ profile. Observations of the SZ increment with SCUBA, which has sufficient sensitivity and resolution for the task, should be straight forward.