The elliptical power law profile lens

Abstract

The deflection, potential, shear and magnification of a gravitational lens following an elliptical power law mass model are investigated. This mass model is derived from the circular power law profile through a rescaling of the axes, similar to the case of a singular isothermal ellipsoid. The resulting deflection can be calculated explicitly and given in terms of the Gaussian hypergeometric function. Analytic expressions for the remaining lensing properties are found as well. Because the power law profile lens contains a number of well-known lens models as special cases, the equivalence of the new expressions with known results is checked. Finally, it is shown how these results naturally lead to a fast and accurate numerical scheme for computing the deflection and other lens quantities, making this method a useful tool for realistically modelling observed lenses.