Determining the cosmic distance scale from interferometric measurements of the Sunyaev-Zel'dovich effect

We determine the distances to 18 galaxy clusters ranging from z ∼ 0.14 to z ∼ 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+4+14-4 -19 km s-1 Mpc-1 for an O M = 0.3, OΛ = 0.7 cosmology, where the uncertainties correspond to statistical followed by systematic at 68% confidence. The best fit H0 is 56 km s -1 Mpc-1 for an open O M = 0.3 universe and 54 km s-1 Mpc -1 for a flat OM = 1 universe. With a sample of 18 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 & XMM-Newton) and available radio observatories (OVRO, BIMA, & VLA). 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, providing a distance ladder independent check on recent constraints on the cosmology of the universe.