Galaxy-lens determination of H0: the effect of the ellipse + shear modelling assumption

Galaxy lenses are frequently modelled as an elliptical mass distribution with external shear and isothermal spheres to account for secondary and line-of-sight galaxies. There is statistical evidence that some fraction of observed quads are inconsistent with these assumptions, and require a dipole-like contribution to the mass with respect to the light. Simplifying assumptions about the shape of mass distributions can lead to the incorrect recovery of parameters such as H[SUB]0[/SUB]. We create several tests of synthetic quad populations with different deviations from an elliptical shape, then fit them with an ellipse + shear model, and measure the recovered values of H[SUB]0[/SUB]. Kinematic constraints are not included. We perform two types of fittings - one with a single point source and one with an array of sources emulating an extended source. We carry out two model-free comparisons between our mock quads and the observed population. One result of these comparisons is a statistical inconsistency not yet mentioned in the literature: the image distance ratios with respect to the lens centre of observed quads appear to span a much wider range than those of synthetic or simulated quads. Bearing this discrepancy in mind, our mock populations can result in biases on H[SUB]0[/SUB] $\sim 10{{\ \rm per\ cent}}$ .