X-ray Detection of the Primary Lens Galaxy Cluster of the Gravitational   Lens System Q0957+561
  Analysis of several recent ROSAT HRI observations of the gravitationally lensed system Q0957+561 has led to the detection at the 3sigma level of the cluster lens containing the primary galaxy G1. The total mass was estimated by applying the equation of hydrostatic equilibrium to the detected hot intracluster gas for a range of cluster core radii, cluster sizes and for different values of the Hubble constant. X-ray estimates of the lensing cluster mass provide a means to determine the cluster contribution to the deflection of rays originating from the quasar Q0957+561. The present mass estimates were used to evaluate the convergence parameter kappa, the ratio of the local surface mass density of the cluster to the critical surface mass density for lensing. The convergence parameter, kappa, calculated in the vicinity of the lensed images, was found to range between 0.07 and 0.21, depending on the assumed cluster core radius and cluster extent. This range of uncertainty in kappa does not include possible systematic errors arising from the estimation of the cluster temperature through the use of the cluster luminosity-temperature relation and the assumption of spherical symmetry of the cluster gas. Applying this range of values of kappa to the lensing model of Grogin & Narayan (1996) for Q0957+561 but not accounting for uncertainties in that model yields a range of values for the Hubble constant:67<H_0<82 km s^-1 Mpc^-1, for a time delay of 1.1 years. 
G. Chartas, D. Chuss, W. Forman, C. Jones, and I. Shapiro