Pseudo Elliptical Lensing Mass Model: Application to the NFW Mass Distribution

Abstract

We introduce analytical expressions for a pseudo fully analytical elliptical projected Navarro, Frenk & White (NFW) mass profile to be used in lensing equations. We propose a formalism that incorporates the ellipticity into the expression for the lens potential, producing a pseudo-elliptical mass distribution. This approach can be implemented to any circular mass profile for which the projected mass profile Sigma(r) and the deflection angle profile alpha(r) both have analytical expressions; however the potential does not necessarily need to take an analytical form. We apply this new formalism to the NFW mass distribution and study how well this pseudo-elliptical NFW model describes an elliptical mass distribution. We conclude that the pseudo-elliptical NFW model is a good description of elliptical mass distributions provided that the ellipticity of the projected mass distribution is <~ 0.4, although with a slightly boxy distribution.