On model-dependent bounds on H(0) from gravitational images Application of Q0957 + 561A,B

Abstract

The images of a background source formed by a foreground mass distribution in a matter-dominated Friedmann cosmology are considered. A transformation is presented that leaves unchanged the image observables, including positions, relative magnifications, apparent luminosities, and differences in propagation times associated with image pairs. The observables are related to the parameters of the source and of a generalized lens model. The transformation is applied to these relations to scale the value of H(0) and to modify the mass distribution of the lens and move the position of the source. One lens model for Q0957 + 561 is discussed in the context of this transformation. The elliptical galaxy G1 is modelled as a singular isothermal sphere, and the light bending of the cluster is represented as a linear function of the impact parameter. It is shown that this model accounts for the positions and relative magnifications of images of Q0957 + 561 and yields a bound on H(0).