Galaxy Cluster Shapes and Systematic Errors in the Hubble Constant as Determined by the Sunyaev-Zel'dovich Effect

Imaging of the Sunyaev-Zei'dovich (S-Z) effect in galaxy clusters combined with the cluster plasma x-ray diagnostics can measure the cosmic distance scale to high accuracy. However, projecting the inverse-Compton scattering and x-ray emission along the cluster line-of-sight will introduce systematic errors in the Hubble constant, H$-O$, because the true shape of the cluster is not known. This effect remains present for clusters that are otherwise chosen to avoid complications for the S-Z and x-ray analysis, such as plasma temperature variations, cluster substructure, or cluster dynamical evolution. In this paper we present a study of the systematic errors in the value of H$-0$, as determined by the x-ray and S-Z properties of a theoretical sample of triaxial isothermal 'beta-model' clusters, caused by projection effects and observer orientation relative to the model clusters' principal axes. The model clusters are not generated as ellipsoids of rotation, but have three independent 'core radii', as well as a random orientation to the plane of the sky.