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The Navarro-Frenk-White (NFW) density profile is often used to modelgravitational lenses. For low values of the characteristic convergence($\kappa_s \ll 1$) of this model - corresponding to galaxy and galaxy groupmass scales - a high numerical precision is required in order to accuratelycompute several quantities in the strong lensing regime. An alternative forfast and accurate computations is to derive analytic approximations in thislimit. In this work we obtain analytic solutions for several lensing quantitiesfor elliptical (ENFW) and pseudo-elliptical (PNFW) NFW lens models on thetypical scales where gravitational arcs are expected to be formed, in the$\kappa_s \ll 1$ limit, establishing their domain of validity. We deriveanalytic solutions for the convergence and shear for these models, obtainingexplicit expressions for the iso-convergence contours and constant distortioncurves (including the tangential critical curve). We also compute thedeformation cross section, which is given in closed form for the circular NFWmodel and in terms of a one-dimensional integral for the elliptical ones. Inaddition, we provide a simple expression for the ellipticity of theiso-convergence contours of the pseudo-elliptical models and the connection ofcharacteristic convergences among the PNFW and ENFW models. We conclude thatthe set of solutions derived here is generally accurate for $\kappa_s \lesssim0.1$. For low ellipticities, values up to $\kappa_s \simeq 0.18$ are allowed.On the other hand, the mapping between PNFW and the ENFW models is valid up to$\kappa_s \simeq 0.4$. The solutions derived in this work can be used to speedup numerical codes and ensure their accuracy in the low $\kappa_s$ regime,including applications to arc statistics and other strong lensing observables.(Abridged)

Analytic Solutions for Navarro--Frenk--White Lens Models for Low Characteristic Convergences