A new model of the gravitational lens 0957+561 and a limit on the hubble constant (vol 464, 92, 1996)

We present a simple mass model for the leasing galaxy in the gravitationally lensed quasar 0957 + 561. We represent the galaxy as a softened power-law sphere (SPLS), a generalization of the singular isothermal sphere with three parameters - ρo, the central density; θC, the angular core radius; and η, the radial index, which is defined such that mass increases as rη at large radius. As in previous studies, we approximate the galaxy cluster surrounding the lensing galaxy by means of a quadratic potential described by its convergence κ and shear γ. A feature of the model is that it does not require a large central compact mass. We fit the model to a recent high-resolution VLBI map of the two images of 0957 + 561. The data provide a number of independent constraints, and the model fit has 6 degrees of freedom, which is a significant improvement over previous models. Although the reduced Χ2 of the best-fit model is only 4.3, nevertheless we obtain a tight constraint on the radial index, 1.07 < η < 1.18, at the 95% confidence level. Thus, the galaxy has mass increasing slightly more rapidly than isothermal (η = 1) out to at least 15 h-1 kpc. Since the light from the galaxy follows a de Vaucouleurs profile, we deduce that the massto-light ratio of the galaxy increases rapidly with increasing radius. We also obtain an upper limit on the core radius, namely θC < 0".11 or linear core radius <330h-1 pc. We use the model to calculate the Hubble constant H0 as a function of the time delay ATBX between the two images. We obtain Ho = (60.5-2.2+5.3)(l - κ)(ΔτBA/1.5 yr)-1 km s-1 Mpc-1 , or = (82.5-3.07.2)(l - κ)(ΔτBA/1.1 yr)-1 km s-1 Mpc-1. Once ATBX is measured, this will provide an upper bound on H0 since K cannot be negative. In addition, the model degeneracy due to K can be eliminated if the one-dimensional velocity dispersion a of the lensing galaxy is measured. In this case, we find that Ho=(60.5-4.1+6.4)(ρ/322km s-1)2(ΔτBA/1.5 yr)-1 km s-1 Mpc-1 , or =(82.5-5.6+8.7)(ρ/322 km s-1)2(ΔτBA/1.5 yr)-1 km s-1 Mpc-1. We find that these results are virtually unchanged if we include the ellipticity of the lensing galaxy or clumpiness of the lensing cluster. © 1996. The American Astronomical Society. All rights reserved'.