Galaxy clusters and cosmology with the Sunyaev-Zel'dovich effect and weak lensing

Sunyaev-Zel'dovich effect (SZE) measurements and weak lensing observations are well-matched in that both probe the projected mass of galaxy clusters. When gas mass fractions derived from SZE-weak lensing comparisons are combined with the hydrostatic method of estimating gas fractions, a direct estimate of the temperature can be made, in a manner that is nearly independent of cosmology. Further assuming a calibrated measure of the gas fraction allows direct distance determinations using only SZE and weak lensing data, without X-ray information. SZE and weak lensing observations are also well matched in terms of the filters that both are applying to the underlying mass distributions. In this work we explicitly show this connection and detail and validate a non-parametric method for calculating gas fractions by combining SZE measurements and weak lensing observations, using the example of interferometric SZE data. The method consists of a comparison of Fourier modes at the spatial scales that have been measured in both the SZE and weak lensing data. We demonstrate the robustness of the method by generating mass maps and SZE images of galaxy clusters from N-body+gas simulations and realistic interferometric observation strategies. We show that current observations should be able to constrain the gas fraction to ∼20% for clusters at redshifts between 0.1 and 1, depending on the accuracy to which the gas temperature and redshift distribution of lensed sources are known. Current data is of a quality which should allow individual determinations of the angular diameter distance to an accuracy of ∼30%.