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

We discuss a method to constrain the intrinsic three-dimensionale 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, with prolate-like shapes being slightly more likely than oblate-like ones; the spherical hypothesis is strongly rejected for most sample members. Cooling flow clusters do not show preferentially regular morphologies.