Models with elliptical potentials (pseudo-elliptical) are often used ingravitational lensing applications. Nevertheless, they generally lead tononphysical mass distributions in some regions. In this paper we revisit thephysical limitations of the pseudo-elliptical Navarro-Frenk-White (PNFW) model,for a broad range of the potential ellipticity parameter \epsilon\ andcharacteristic convergence \kappa_s focusing on the behavior of the massdistribution close to the tangential critical curve, where tangential arcs areexpected to be formed. We investigate the shape of the mass distribution onthis region and the presence of negative convergence. We obtain a mapping fromthe PNFW to the NFW model with elliptical mass distribution (ENFW) and providefitting formulae for connecting the parameters of both models. We compare thearc cross section for these models using the "infinitesimal circular sourceapproximation". We find that the PNFW model is well-suited to model anelliptical mass distribution on a larger \epsilon\ - \kappa_s parameter spacethan previously expected. In particular values as large as \epsilon\ ~ 0.65 areallowed for small \kappa_s. However, if we require the PNFW model to reproducethe arc cross section of the ENFW well, the ellipticity is more restricted. Wealso find that the negative convergence regions occur far from the arcformation region and should therefore not be a problem for studies withgravitational arcs. The determination of a domain of validity for the PNFWmodel and the mapping to ENFW models could have implications for the use ofPNFW models for the inverse modeling of lenses and for fast arc simulations.
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