Systematic uncertainties in gravitational lensing models: a semi-analytical study of PG1115+080

Abstract

While the Hubble constant can be derived from observable time delays between images of lensed quasars, the result is often highly sensitive to assumptions and systematic uncertainties in the lensing model. Unlike most previous authors we explore a broad class of models with non-parametric lens radial profile and allow for non-elliptical lens potentials. The axis ratio and position angle of the lens can be determined from the image positions of quadruple gravitational lensed systems by solving the lens equation semi-analytically, independent of the radial profile. We give simple equations for estimating the power-law slope of the lens density directly from the image positions and for estimating the time delay ratios. Our method greatly simplifies the numerics for fitting observations and is fast in exploring the model parameter space. As an illustration we apply the model to PG1115+080. We show that the measured image positions and time delays do not uniquely determine the Hubble constant. The mass-to-light ratio of the lens galaxy increases with radius, higher at image C than at image B.