New modeling of the lensing galaxy and cluster of Q0957+561: Implications for the global value of the hubble constant

The gravitational lens 0957 + 561 is modeled utilizing recent observations of the galaxy and the cluster as well as previous VLBI radio data that have been reanalyzed recently. The galaxy is modeled by a power-law elliptical mass density with a small core, while the cluster is modeled by a nonsingular power-law sphere, as indicated by recent observations. Using all of the currently available data, the best-frt model has X-min(2)/N-dof approximate to 6, where the chi(2) value is dominated by a small portion of the observational constraints used; this value of the reduced chi(2) is Similar to that of the recent FGSE (Falco, Gorenstein, & Shapiro elliptical) best-fit model of Barkana et al. However, the derived value of the Hubble constant is signficantly different from the value derived from the FGSE model. We find that the value of the Hubble constant is given by H-0, = 69(-12)(+18)(1 - K) and 74(-17)(+18)(1 - K) km s(-1) Mpc(-1) with and without a constraint on the cluster's mass, respectively, where k is the convergence of the cluster at the position of the galaxy and the range for each value is defined by Delta chi(2) = chi(min)(2)/N-dof. At present, the best achievable fit for this system is not as good as for PG 1115+080, which has also recently been used to constrain the Hubble constant, and the degeneracy is large. Possibilities for improving the fit and reducing the degeneracy are discussed.