Fast Calculation of Gravitational Lensing Properties of Elliptical Navarro-Frenk-White and Hernquist Density Profiles

Abstract

We present a new approach for fast calculation of gravitational lensing properties, including the lens potential, deflection angles, convergence, and shear, of elliptical Navarro-Frenk-White (NFW) and Hernquist density profiles, by approximating them by superpositions of elliptical density profiles for which simple analytic expressions of gravitational lensing properties are available. This model achieves high fractional accuracy better than $10^{-4}$ in the range of the radius normalized by the scale radius of $10^{-4}-10^3$. These new approximations are $\sim 300$ times faster in solving the lens equation for a point source compared with the traditional approach resorting to expensive numerical integrations, and are implemented in {\tt glafic} software.