The cross-correlation of Sunyaev-Zeldovich effect (SZ) and weak-lensing imaging surveys can be used to test how well hot baryons trace dark matter in clusters of galaxies. We examine this concept using mock SZ and weak-lensing surveys based on the forthcoming AMiBA experiment and generated from a pre-heated cosmological N-body/hydrodynamic simulation. A cross-correlation diagram between matched lensing convergence and Compton y maps exhibits butterfly-wing-like structures, corresponding to individual clusters, that encode rich information about the distributions of hot gas and dark matter. When the cluster redshift and temperature are available the slope of a wing reveals the cluster gas fraction and the width of the wing indicates how badly the hot gas traces dark matter. On the basis of simulated data we discuss systematic errors in the projected gas fraction estimates that would be obtained from such survey comparisons.
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