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 temper-ature decrements. The sample turns out to be slightly biased, with strongly elon-gated clusters preferentially aligned along the line of sight. This result demon-strates 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 ex-hibit a marked triaxial structure; the spherical hypothesis is strongly rejected for most sample members. Cooling flow clusters do not show preferentially reg-ular 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