Effect of gravitational lensing on measurements of the Sunyaev-Zeldovich effect

The Sunyaev-Zeldovich (SZ) effect of a cluster of galaxies is usually measured after background radio sources are removed from the cluster field. Gravitational lensing by the cluster potential leads to a systematic deficit in the residual intensity of unresolved sources behind the cluster core relative to a control field far from the cluster center. As a result, the measured decrement in the Rayleigh-Jeans temperature of the cosmic microwave background is overestimated. We calculate the associated systematic bias that is inevitably introduced into measurements of the Hubble constant using the SZ effect. For the cluster A2218, we find that observations at 15 GHz with a beam radius of 0.4' and a sourer removal threshold of 100 mu Jy underestimate the Hubble constant by 7%-13%. If the profile of the gas pressure declines more steeply with radius than that of the dark matter density, then the ratio of lensing to SZ decrements increases toward the outer part of the cluster.