Measuring the Hubble constant from Ryle Telescope and X-ray observations, with application to Abell 1413

We describe our methods for measuring the Hubble constant from Ryle Telescope (RT) interferometric observations of the Sunyaev–Zel'dovich (SZ) effect from a galaxy cluster and observation of the cluster X-ray emission. We analyse the error budget in this method: as well as radio and X-ray random errors, we consider the effects of clumping and temperature differences in the cluster gas, of the kinetic SZ effect, of bremsstrahlung emission at radio wavelengths, of the gravitational lensing of background radio sources and of primary calibration error. Using RT, ASCA and ROSAT observations of the Abell 1413, we find that random errors dominate over systematic ones, and estimate for a an ΩM=1.0, ΩΛ=0.0 cosmology.