Measuring the Three-Dimensional Structure of Galaxy Clusters. II. Are clusters of galaxies oblate or prolate?

The intrinsic shape of galaxy clusters can be obtained through a combination of X-ray and Sunyaev-Zeldovich effect observations once cosmological parameters are assumed to be known. In this paper we discuss the feasibility of modelling galaxy clusters as either prolate or oblate ellipsoids. We analyze the intra-cluster medium distribution for a sample of 25 X-ray selected clusters, with measured Sunyaev-Zeldovich temperature decrements. A mixed population of prolate and oblate ellipsoids of revolution fits the data well, with prolate shapes preferred on a 60-76% basis. We observe an excess of clusters nearly aligned along the line of sight, with respect to what is expected from a randomly oriented cluster population, which might imply the presence of a selection bias in our sample. We also find signs that a more general triaxial morphology might better describe the morphology of galaxy clusters. Additional constraints from gravitational lensing could disentangle the degeneracy between an ellipsoidal and a triaxial morphology, and could also allow an unbiased determination of the Hubble constant.