Systematic effects in lens inversions - Aleph(1) exact models for 0957 + 561

Abstract

Due to the careful study of its VLBI structures, the gravitational lens 0957 + 561 is the most accurately characterized of the lens candidates. Nonetheless, the observational data supplies only five firm constraints, compared to a minimum of nine free parameters in simple models for the lens using an elliptical galaxy and an elliptical cluster both with fixed radial structure. This paper examines the systematic variations between models for the lens potential that satisfy the constraints exactly. This is done using both the 4 degrees of freedom left when the radial structure of the galaxy is fixed, as well as variations due to changes in the radial structure. The systematic variations between the models allow for a range of time delays from approximately 0.1h^-1^ to 1.0h^-1^ yr for a fixed Einstein-de Sitter cosmology if the galaxy and the cluster satisfy the velocity dispersion constraints of 240 <~σ_g_<~ 320 km s^-1^, and 500<~σ_c_<~ 1500 km s^-1^, and the center of the cluster lies within 30" of the galaxy. Given the formal value for the velocity dispersion (303 +/- 50 km s^-1^) and the measured time delay (1.3 +/- 0.1 yr), I find that h <~ 0.6 +/- 0.2 considering only the observational errors in the velocity dispersion. However, there are large uncertainties in the relationship between the observed velocity dispersion and the mass distribution. For example, the presence of a dark matter halo which raises the velocity dispersion which characterizes the mass by a factor of (3/2)^1/2^ relative to the observed velocity dispersion, formally increases the value of the Hubble constant to h <~ 0.9 +/- 0.3, although the + 0.3 error bar is probably an exaggeration. Even with a known velocity dispersion, uncertainties in other parameters of the system, such as the principal axis of the mass distribution in the galaxy, can also introduce large uncertainties into the time delay. Because the images in 0957 + 561 only weakly constrain the mass distribution of the lens, the 0957 + 561 system can be used to measure the Hubble constant only to the accuracy with which observational parameters such as central velocity dispersion, ellipticities, and orientations can be translated into information on the mass distribution in the system. This systematic problem is the ultimate limitation on the measurement, and the statement that the 0957 + 561 system can measure H_0_ to a given level of accuracy is equivalent to the claim that the mass distribution in the lens galaxy or cluster is understood to the same level of accuracy.