Measuring the three dimensional structure of galaxy clusters. 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-Zeldovich observations. The method is applied to a sample of 25 X-Ray selected clusters, with measured Sunyaev-Zeldovich 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-Zeldovich effect and X-Ray surface brightness, can provide a simultaneous determination of the three dimensional structure of a cluster, of the Hubble constant, and the cosmological energy density parameters