Determining the Cosmic Distance Scale from Interferometric Measurements of the Sunyaev-Zel'Dovich Effect

The distances to eighteen galaxy clusters are determined, with redshifts ranging from z approx. 0.14 to z approx. 0.78 from a maximum likelihood joint analysis of 30 GHz interferometric Sunyaev-Zel'dovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal beta model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. These distances imply a Hubble constant of 60((sup +4+13)(sub -4-18)) km s(exp -1) megaparsec(exp -1) for an Omega(sub M) = 0.3, Omega(sub Lambda) = 0.7 cosmology, where the uncertainties correspond to statistical followed by systematic at 68% confidence. With a sample of eighteen clusters, systematic uncertainties clearly dominate. The systematics are observationally approachable and will be addressed in the coming years through the current generation of X-ray satellites (Chandra & XMIM-Newton) and radio observatories (OVRO (Owens Valley Radio Observatory), BIMA (Berkeley Illinois Maryland Association), & VLA (Very Large Array)). Analysis of high redshift clusters detected in future SZE and X-ray surveys will allow a determination of the geometry of the universe from SZE determined distances.