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Weak lensing and the Sunyaev-Zel'dovich effect (SZE) are each measures of the projected mass distribution of galaxy clusters. Weak lensing is probing the projected total mass, while the SZE is probing the projected (temperature-weighted) gas distribution. Direct comparisons of the two distributions should allow determinations of the gas mass fraction and the gas temperature. With a local calibration of the true gas fraction, it should be possible to estimate angular diameter distances to clusters as well. Interferometric measurements must be handled carefully, however, with the proper analysis done in the Fourier domain, rather than on the reconstructed images. We present a non-parametric method for comparing the SZE and mass distributions that properly accounts for the finite fields of view of both the interferometer and the weak lensing shear measurements. At the sensitivity limits of current instruments, we estimate that the gas fraction can be determined to an accuracy better than $20\%$ if the gas temperature is known from other methods, while the temperature can be estimated to a comparable precision if the redshift distribution of lensed sources is approximately known. |
