The elliptical power law profile lens

TL;DR

This paper introduces an elliptical power law profile lens model for gravitational lensing, providing explicit formulas for lensing properties, which enhances modeling accuracy and computational efficiency.

Contribution

It derives explicit analytical expressions for lensing quantities of an elliptical power law profile, improving modeling flexibility and computational speed in gravitational lensing studies.

Findings

Explicit formulas for deflection, potential, shear, and magnification.

Validation of new expressions against known models.

Development of a fast numerical scheme for lens calculations.

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.