The lensing properties of the Sersic model

It is well known that the surface brightness of elliptical galaxies and of bulges of spiral galaxies is best fitted by the Sersic r(1/n). profile. It is thus interesting to explore the lensing properties of the Sersic model because of its wide range of applicability. To this aim, we evaluate the lensing potential, the deflection angle, the time delay between the images and the amplification for a circularly symmetric lens whose surface density is described by the Sersic profile. We estimate the same quantities also adding a shear term to the deflection potential in order to study (at the lowest order) the impact of deviations from radial symmetry or the contribution from other nearby lenses. Moreover, we investigate the systematic errors due to the use of a de Vaucouleurs profile instead of the correct Sersic model also taking into account the presence of a dark halo.