Model-dependent bounds on H0 from gravitational images: Application to Q0957+561A,B

We consider the images of a background source formed by a foreground mass distribution in a matter-dominated Friedmann cosmology. We present a transformation that leaves observable properties of these gravitational images invariant; superposing a uniform, projected mass distribution on the initial mass distribution, combined with moving the source position and reducing the value of H0, both by an appropriate scale factor, leaves unchanged the positions, relative magnifications, apparent luminosities, and difference in propagation times associated with any two images of the source. Using a compound mass distribution to represent a galaxy-cluster lens, we can account for the positions and relative magnifications of the A and B images of Q0957+561. Since mass cannot be negative, the transformation applied to this lens model yields bounds on the Hubble constant, given the difference Δtau/sub BA/ (in years) between the propagation times associated with the two images: 0<H0< or =(98 +- 3)Δtau-1/sub BA/ km s-1 Mpc-1. Temporal variations in the quasar's luminosity always appear first in the A image. Measurements of any such variations, reliably correlated between images, would determine Δtau/sub BA/. We emphasize that this transformation applied to other plausible lens models may not yield such bounds on H0