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 H0. 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 H0. 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 H0$\sim 10{{\ \rm per\ cent}}$.