ar X iv : a st ro - p h / 99 09 29 1 v 1 1 6 Se p 19 99 Degeneracies of the radial mass profile in lens models

We discuss a simple parameter degeneracy in lens models which follows directly from the well known mass sheet degeneracy and prevents determining the radial mass distribution from lensing alone for many systems. For cosmological important systems like 1115+080 it is shown that no exact value of H0 can be determined without assuming a mass index β. 1. The mass sheet degeneracy The degeneracies examined in this poster are a consequence of the so called “mass sheet degeneracy”. Falco et al. (1985) and Gorenstein et al. (1988) have shown that a lens model can be transformed to an equivalent model by scaling it with a factor of (1−κ) and adding a constant surface mass density κ. Constant mass densities as well as external shear do not contribute to the time delay. As H0 ∆t depends linearly on the mass density, H0 also scales with (1−κ). This has the effect that only an upper limit for H0 can be determined when additional mass sheets may be present. When modelling lens systems, no decision between different models can be made if the models are equivalent just for the positions of the observed images. We want to examine the impact of the degeneracy for simple parametric lens models. 2. Perturbed spherical lens models We use the very simple approach of a spherically symmetric mass distribution plus external shear γ to illustrate the degeneracy. For a a radial deflection angle of α(r) we can find an equivalent model by scaling α(r) and the shear by (1−κ) and adding the surface mass density which gives a contribution of κ r to the radial deflection angle. Whether this leads to a degeneracy of model parameters, depends on the number of images, the image configuration and the number of parameters used to describe the radial deflection angle α. 1 email: [email protected] 2 email: [email protected]