Measuring the Three-dimensional Structure of Galaxy Clusters. I. Application to a Sample of 25 Clusters

We discuss a method to constrain the intrinsic shapes of galaxy clusters by combining X-ray and Sunyaev-Zel'dovich observations. The method is applied to a sample of 25 X-ray-selected clusters, with measured Sunyaev-Zel'dovich temperature decrements. The sample turns out to be slightly biased, with strongly elongated clusters preferentially aligned along the line of sight. This result demonstrates that X-ray-selected cluster samples may be affected by morphological and orientation effects, even if a relatively high threshold signal-to-noise ratio is used to select the sample. A large majority of the clusters in our sample exhibit a marked triaxial structure; the spherical hypothesis is strongly rejected for most sample members. Cooling-flow clusters do not show preferentially regular morphologies. We also show that identification of multiple gravitationally lensed images, together with measurements of the Sunyaev-Zel'dovich effect and X-ray surface brightness, can provide a simultaneous determination of the three-dimensional structure of a cluster, of the Hubble constant, and of the cosmological energy density parameters.