Gravitational Lensing By an Ellipsoidal Navarro-Frenk-White Halo

Dark-matter halos with a triaxial ellipsoidal symmetry yield elliptically symmetric surface-density distributions when integrated along the line of sight. We explore here gravitational lensing by such a halo with a Navarro–Frenk–White density profile, parameterized by a convergence parameter, eccentricity, and scale semimajor axis. We present exact analytical formulas for the components of the deflection angle valid for arbitrary eccentricity. Using these results, we compute the lens shear and demonstrate its properties. We illustrate the different geometries of the critical curves and caustics, and plot their characteristic dimensions and areas as a function of eccentricity for representative values of the convergence parameter. The obtained results can be employed in simulations and analyses of strong lensing by galaxies and galaxy clusters.