A Measurement of the Hubble Constant from Sunyaev-Zel'dovich Effect and X-ray Images of Galaxy Clusters

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With analysis of Sunyaev-Zel'dovich effect and x-ray data it is possible to determine the distances to galaxy clusters. Cosmic microwave background (CMB) photons inverse Compton scatter off of the hot intracluster medium (ICM) causing a small distortion in the CMB spectrum, the Sunyaev-Zel'dovich (SZ) effect. The SZ effect is proportional to the pressure integrated along the line of sight ~ int n_e T_e dl and appears as a small ( ~ 1 mK) decrement at centimeter wavelengths. The ICM also emits at x-ray wavelengths with a signal ~ int n_e(2) T_e(1/2) dl for bremsstrahlung radiation. Taking advantage of the different dependencies on the electron density, n_e, one can solve for the size of the cluster. One then has a ruler with which to measure the angular diameter distance to the cluster, independently of the distance ladder. We present our method and distances for a sample of our imaged SZ effect clusters. We use our interferometric cm-wave observations of the SZ effect at the BIMA and OVRO observatories and archival ROSAT x-ray data. We perform a maximum likelihood fit to the SZ and x-ray data simultaneously using an isothermal spherical beta -model. These fits yield information about the shape and density of the ICM. We can then use these clusters to determine the Hubble constant. The largest source of observational uncertainty in H_deg, ~ 20%, is the x-ray determined electron temperature. Possible systematics are discussed, the largest being the assumption of isothermality for the ICM. The Chandra observatory will greatly reduce the uncertainty in T_e and be able to detect temperature gradients as well as provide greater spatial resolution. ER acknowledges support by NASA GSRP Grant NGT-50173.

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